+ its close relative the Ouvea parakeet, but it is much rarer and as far as I know none in North America.
Among the New Caledonian reptiles, a few are common in captivity, both privately and in zoos: gargoyle, crested and New Caledonian giant geckos, but there are also smaller numbers of some of the others geckos.
It seems there is very little interest (by zoos or privates) in the skinks from New Caledonia and consequently they're virtually absent from captivity. This "popular gecko vs. unpopular skink" pattern is mirrored by the New Zealand species, though there are far fewer New Zealand geckos than New Caledonian geckos in captivity.
There has been no mention of fish in earlier posts, but a review of what is kept outside the native range can be done quite fast: None of the relatively few freshwater fish species of New Zealand and New Caledonia are kept elsewhere. None of New Caledonia's endemic marine fish are kept elsewhere, but species that are found more widely in the Coral Sea are fairly regular in coral reef aquariums. I'm only aware of a single aquarium outside New Zealand with endemic/near-endemic marine fish from that country: Osaka (Japan) has fairly big Cook Strait aquarium with quite a range of species. There are a few old-ish photos from the tank
here (the tank now also holds loggerhead sea turtle).
BTW, contrary to the suggestion in the first post of this thread, the New Caledonian crow is not the only species of corvid that has been observed to use tools in the wild. It is, however, by far the one where tool use has been most extensively studied and seemingly also the one that uses it most frequently. You don't have to leave your homestate of Texas to see corvids that are known to use tools:
American crow and
green jay.