@Hyak_II, besides bottlenose dolphins, what are some other "durable" cetacean species? I'm guessing beluga, harbor porpoise, maybe Commerson's?
There are actually a number of different species that do fairly well!
The stables of the industry are of course the most durable. Pacific, Altantic, Black Sea and Indo-Pacific Bottlenose Dolphins all adapt extremely well to life under human care, regularly meet and exceed wild lifespans, and show excellent reproductive success. Populations of Atlantic Bottlenose in Europe and North America are at the state they are totally self sustaining, to the point that there are now animals bred to the 5th generation captive bred. However all 4 species/subspecies have actively breeding populations throughout the world.
Belugas do fairly well, but they come with their own set of issues. They seem to be much more prone to illnesses than more southerly species, and when they get sick they can succumb much more easily to whatever is ailing them. Additionally, they have fairly limited breeding success, and seem to fair much better breeding wise when housed in larger groups, something that is not often catered to. They are also suffering from a lack of founders in North America in co-operating facilities. To put it in perspective, in the US there are currently 27 animals, with 6 (possibly10) founding male lines (only 4 of which have breeding success), and 10 founding female lines, most of which are breeding, luckily. There are usually 1-2 calves born every 2 years. In comparison, at Marineland in Canada, there are 7 founding male lines,and some 18-19 founding females, at least 14 of which are already breeding, and this is all at one park!
Like @littlewallaby mentioned, Orca also do very well. For the past 20 or so years they have enjoyed very good survival rates, excellent reproductive success, and have generally been thriving. They are extremely smart, and within the top 5 species that adapts best to captivity. Were it not for their large size, expense of care, and public controversy, (mainly the latter 2) I have no doubt they would be far more common in zoological collections.
Pacific Whitesided Dolphins also do fairly well. They, much like the belugas, suffer from an EXTREMELY limited founder base (like really bad, there is only 1 founding male and 6 founding females left, all are older, 1 has never bred, 1 is post reproductive, and 1 is both). All the others are captive bred, and all are sired by one of two males (the living founder and another deceased male) with the exception of one, he was conceived via artificial insemination with a Japanese male, but is a grand offspring to the deceased founding male, and is related to a number of the living females). However other than limited genetics, they have decent life spans, reasonable breeding success, and also adapt well to captive life.
Finless Porpoises and Commerson's Dolphins are two others that actually do surprisingly well! Both have fairly good longevity and breeding success under human care (commerson's especially, virtually every animal given the chance to breed has produced offspring), and their small size makes housing them fairly easy. Japan is the stronghold for them, as they are the only country breeding Commerson's and the main breeder of captive Finless Porps as well.
Harbor Porpoises do alright, but they seem to be a tad on the more sensitive side and have limited breeding success, however virtually all animals (sans 1 captive bred female in Europe) in captivity currently are rescues, which no doubt gives them a disadvantage for long term success.
Other species that generally do well with proper husbandry, but aren't kept in large numbers include Pseudorca, Short Finned Pilot Whale, Rough Toothed Dolphin, Risso's Dolphin, and Amazon River Dolphin.