We are also rhino obsessed! We didn't see them last time on the Safari ride, but we had all previous times. We went late morning last time. The best viewing we had was a late afternoon ride - one of the last of the day. We were in the later part of the ride and hadn't seen any, and then suddenly we came upon 2 really close, and they were jumping around kind of playing.
Also on the train to Rafiki's planet watch, you go past the rhino barns. We could see some inside the barns (it's not great viewing but still we could see them), and that kind of made up for not seeing them on the safari ride.
We got a stuffed rhino from one of the shops on discovery island back in 2012. I looked last trip (a year ago) and didn't see any stuffed rhinos in that same store. You could always get one off
Amazon, and leave it staged in the room. Then if you can't find one in AK, you come back and find that Mickey must have brought one to the room. Or if you do find one in AK, then it's got a rhino friend when you get back to the room.
Also keep your eyes open for the rhino in It's a Small World.
For other trips, we have founds some zoos have "feed a rhino" (for a fee). We fed some leaves to a rhino at Zoo Miami several years ago and that was really neat.