Maybe you like long-shots. If so, go to the IUCN Red List and search for species that are critically endangered (3,565 worldwide), or extinct in the wild (63 unfortunate species). The aforementioned amphibians, 488 of which are critically endangered or surviving only in captivity, are particularly compelling candidates.
Or think locally. The Red List includes 8,884 endangered species in the United States, and you can even search by state. The Lantern is particularly fond of the black-footed ferret, which has come back from extinction and now feasts on unsuspecting prairie dogs in the Western states. Once you find a good candidate, look for local groups or university researchers, many of whom are desperate for donations of any size. Even $50 can help them feed captive breeding populations, monitor individuals in the wild, or trap invasive predators like the brown tree snakes that decimated Guam's bird population. (Be aware that some conservationists think you'd be better directing your money to places with a greater density of threatened species, like Madagascar or Indonesia, than keeping it in the relatively nonbiodiverse United States.)
The Lantern understands the appeal of trying to save a single species, but general habitat preservation will typically get you the most bang for your buck. This usually means buying up and reforesting degraded land. You might want to focus on biodiversity hotspots, where some of the world's most important species live. If you're looking to give your child something tangible, consider SavingSpecies.org. The group will send you a Google Earth image of your habitat purchase to show your kids the reforestation process. If your child absolutely must have the plush toy, pick up a Golden Lion Tamarin. Scientists aren't above using these so-called "mascot" or "charismatic" species to rope in donors.
In general, your best bet is to stick with reputable organizations like major conservation groups, universities, or government-sponsored programs. No species-saving project is guaranteed to succeed, but there are plenty of reasons to be optimistic. Captive breeding organizations like the Peregrine Fund, for example, nursed the peregrine falcon from DDT-induced near extinction just decades ago to removal from the endangered species list. Other success stories abound.
Donate early, donate often, and consider spreading your money across different species. Plush toys are decidedly nonendangered.
The Green Lantern thanks Felicity Arengo of the American Museum of Natural History, Resit Ackakaya of Stony Brook University, Madeleine Bottrill of the University of Queensland, Georgina Mace of Imperial College in London, John Marzluff of the University of Washington, Stuart Pimm of Duke University, Phil Rainbow of the Natural History Museum in London, Rod Sayler of Washington State University, and David Wilcove of Princeton University.