Wikipedia might be useful here as a general reference.
The entire period of time we've talked about is encompassed by the Phanerozoic epoch (545 mya to present).
http://en.wikipedia.org/wiki/Phanerozoic
The Phanerozoic is divided into three eras:
Paleozoic (545-250 mya): rudist and tabulate corals were major reef builders as were a number of other critters which generally aren't that went extinct or aren't that important today. Scleractinian corals didn't exist yet, but their ancestors probably started to show up near the end of this period.
http://en.wikipedia.org/wiki/Paleozoic
Mesozoic (250-65 mya): the Paleozoic ends with huge extinction that really monkies things up. The Mesozoic consists of the Triassic, Jurassic, and Cretaceous periods. Dinosaurs originate in the middle Triassic, and we have are first undisputable scleractinian corals (modern stony corals). There are extinction events at the end of the Triassic and Jurassic. Corals hit a hickup, but keep on trucking. During the Cretaceous reef-building slows way down, probably due to changes in sewater chemistry. At the end of the Cretaceous most species on Earth die, including the dinosaurs (minus birds). Coral diversity declines substantially, but they survive.
http://en.wikipedia.org/wiki/Mesozoic
Cenozoic (65 mya to present): 10 million years in there is a major geologic event (Paleocene Eocene Thermal Maximum) that causes rapid global warming and ocean acidification (though probably much slower than is currently happening). Coral reefs pretty much disappear for 5 million years, but the survivors eventually pop back up and resume reef-building as conditions improve globally. Reef-building by primarily scleractinian corals, coralline algae, and some green alage (e.g., Halimeda) is pretty strong until present.
http://en.wikipedia.org/wiki/Cenozoic
Hope that helps.
Chris