But before we can get to the famous species, let's have a quick look at some dubious specimens, which we're not quite sure where they fit, and then the earliest appearing group—the sinraptors, or metriacanthosaurs.
Becklespinax altispinax. This guy was a very early discovered dinosaur; known only from a few vertebrae, but described by Richard Owen himself, in 1856. Although originally referred to Megalosaurus (but seriously; what wasn't?) this confusion is what led to the hump on the back of the plodding Benjamin Waterhouse Hawkins sculpt of the animal that appeared famously in the Crystal Palace. Becklespinax had relatively tall neural spines on the vertebrae, which mesmerized later describers who have tried to refer it to Acrocanthosaurus as well. It comes from the Wealdon Group of the early Cretaceous Varanginian (about 130-140 million years ago) in southeastern England. His contemporaries would be a number of poorly known yet ironically very famous dinosaurs, who include most of the first dinosaurs named or described: Iguanodon, Hylaeosaurus, Cetiosaurus, etc.
It's probably not really very primitive, given the time frame in which it appears, but it's so poorly known that we can't really determine what Becklespinax is. It might not even be a carnosaur at all; it might be a "megalosaur" or other more primitive tetanuran.
Gasosaurus constructus. Another poorly known critter, Gasosaurus is known from the lower Shaximiao formation (164 million years ago) in Sichuan, and is poorly enough known that it's placement on the family tree is also uncertain. It was probably relatively small, and it may have been a basal tetanuran, basal carnosaur—related to the sinraptors (probably the most likely, given its temporal and geographical placement) or even a basal coelurosaur. In its environment there are a lot of stegosaurs, a number of basal ornithischians (like fabrosaurs) or early ornithopods (primitive hypsilophodonts) as well as sauropods like Shunosaurus and Omeisaurus.
Erectopus superbus. A young carnosaur, from the La Penthiève beds in France from the lower Cretaceous, the exact time and placement in the family tree of this guy is unknown. It is very late appearing for a carnosaur, and it does appear to be definitely a carnosaur, but other than that, very little is known of it. It appears to have been found in a formation that was semi-marine; either an island or because it washed out to sea; other fossils found with it include plesiosaurs, ichthyosaurs, and marine crocodiles. Like every other meat-eating dinosaur discovered within the 1800s, it was known as Megalosaurus for quite some time.
The first actual family within Carnosauria that we encounter are the sinraptors. Sinraptoridae has largely been ousted as the name Metriacanthosauridae appears to have precedence, but typing the informal "sinraptors" is a heckuva lot easier. As you can probably guess from the name, they are mostly found in China, and tend to be early to late Jurassic, making them the earliest appearing solid group of carnosaurs. If one can speak about the group generically, it would be fair to call them allosaur-like therapods, both in shape and in size, but with a tendency towards tall backbone spines. This tendency was repeated by some of the later appearing carcharodontosaurs, and was of course even more famous in the spinosaurs, which are not carnosaurs at all. Some of the ornithopods also tended towards this trait, which seems to have been one that appeared repeatedly and independently in various dinosaur families that were not related to each other.
Xuanhanosaurus qilixiaensis. Quite a mouthful, as are many of the Chinese dinosaurs. Known from some partial sub-cranial skeletal elements, this was originally believed to be a megalosaur, but more recently it has been recovered as a basal sinraptor; although it is a "wildcard" taxa that tends to make phylogenies unstable and weird. Found in the same formation as Gasosaurus (although their temporal relationship is not understood) it was a relatively smallish animal; maybe 15 feet long (which is actually slightly larger than the specimen of Gasosaurus known) and seems to have had an unusually large and strong forelimb. The describer, Dong Zhiming, even proposed that it might have been quadrupedal, although that idea, fanciful and interesting as it seemed, has not been accepted by anyone else. Although, if you look, you can find illustrations online of what some have thought that would look like—quite an interesting idea.
Yangchuanosaurus shangyouensis. Also, Y. magnus, which is no longer considered a separate species. From a little earlier than Allosaurus itself (although the exact timing of its formation is subject to some contradictory data), Yangchuanosaurus was not only very similar in size and shape to North American Allosaurus, but also appeared very close to it in time, and rambled through a faunal assemblage of similar creatures as the Morrison—the Shangshaximiao Formation has stegosaurs, ornithopods, large sauropods, crocodiles, small therapods, etc. The largest specimen was estimated to be about 35 feet long; fairly big, although the type specimen was only about 26 feet long.
A number of other dubious specimens, with various names, were determined just in the last few years by Carrano, Benson and Sampson to belong to a different species of the same genus, Y. zigongensis. This animal appears just a bit earlier than Y. shangyouensis and is likely ancestral to it. This makes it very close in time to Xuanhanosaurus and Gasosaurus, if not coterminous. Exactly why there were so many closely related (apparently) creatures in the same time and place is unclear. Sadly, the most likely interpretation is that the colorful names "Szechuanosaurus" and "Szechuanoraptor" are no good. Too bad.
All of the Yangchuanosaurus species appear to have had a highly ornamented head, with a bony ridge along the nose and multiple hornlets. This is often forgotten; most of the therapods have highly decorated heads, really, but the nose ridge was quite tall and almost Ceratosaurus-like; although of course those two are also not closely related.
The rest of this group are all part of a subfamily within the sinraptors (Metriacanthosauridae) called Metriacanthosaurinae, which includes four genera. Three of them are Chinese.
Metriacanthosaurus parkeri. Of course, this was originally named Megalosaurus parkeri but was later renamed Altispinax. Although named for its neural spines, they are not really all that high compared to many other therapods, and are certainly much more modest than that of Acrocanthosaurus. Known only from a partial hip, leg and some vertebrae, Metriacanthosaurus is about the same size as an average Allosaurus specimen from the Morrison. It comes from the Oxford Clay Formation from the... wait for it... Oxfordian period, coterminous with the early Morrison. Although much of the material referred to this formation (dinosaur-wise, at least) is pretty scanty, it looks to be a typical late Jurassic fauna in most respects. Lots of fish and invertebrates, on the other hand, are known from the Oxford Clay.
Shidaisaurus jinae. Poorly known, and from a specimen that is probably sub-adult to boot, very little can be said about Shidaisaurus other than its clear familial relationship, modest size and that it comes from the Upper Lufeng in the early Jurassic—although various authors vary in how they characterize exactly when this means that it lived. Some papers refer to it as a basal tetanuran rather than a sinraptor, but the Carrano, Brusatte and Benson paper recovers it as a metriacanthosaurine.
Sinraptor dongi. Often given short shrift as a rather "boring" representative of the allosaur clade, Sinraptor appears to have been a medium sized therapod; a bit smaller than Yangchuanosaurus which was in turn a bit smaller than Allosaurus, lacking in head gear of any notable type, there's not a lot that really stands out, I admit. About 25 feet long (although if we had more samples, we may find that it could grow larger—there is a spectacularly large tooth that may belong to Sinraptor found in this area that would be considerably larger than the specimens we know, if so), and found in the Shishugou Formation (known to us already as the home of Guanlong the early tyrant) the most interesting thing about Sinraptor is really the environment that it is found in. Slightly earlier than the Morrison, although very broadly similar to it, we have a number of classic dinosaur elements here; Sinraptor as a carnosaur, large sauropods (Mamenchisaurus, a camarasaur), an ornithopod that little is known about, a medium sized stegosaur, early alvarezsaurs, a noasaur, a few other small therapods, etc. One of the earliest tyrannosaurs and the earliest ceratopsian are located here. Sinraptor may have replaced Monolophosaurus, a "megalosaur" with a large nose crest that appears in the earliest part of the formation.
There may have been more than one species as well; "Sinraptor" hepingensis is a specimen that's bounced around in various genera over the years, and appears to be closely related to Sinraptor although slightly more basal.
Sinraptor is also famous for some paleopathology, specifically some broken ribs and what appear to be bite marks on the skull. Some have argued for cannibalism based on these, but more likely it was intraspecific competition. It's well known that a number of therapods fought via face-biting, and most survived the combat to partially heal their wounds.
Siamotyrannus isanensis. One of the few dinosaurs known from Thailand (and named for Siam, the older kingdom of the Thai people, it is a modest-sized 20 or so foot carnosaur. We think. Some early analysis presumed it was actually a tyrannosauroid, and later a basal carnosaur. The phylogenies of Brusatte, Carrano and Benson seem confident in its placement as a metriacanthosaurine, however. Since it's only known from part of a hip and some back and tail vertebrae, in some ways, we don't have a ton to go on. A tibia and some teeth were also referred to the species, but I'm always skeptical that those are correct, since the only reason to believe so is there general spatial relationship. It comes from the Sao Khua formation; an early Cretaceous formation about 129 million years old—which would make this by far the latest appearing sinraptor. It's neighbors would be a spinosaurid (known only from some teeth), a titanosaurian and other incertae sedis sauropod remains, an ornithomimosaur, and other uncertain therapods.