This is probably a dumb question, but how do you actually make these images? Is there a site or a program for AI-generated furry NSFW?

Late to this, but, might as well put it here for others who might try looking here.
Look into: CivitAI, Automatic1111, and Stable-Diffusion. There's a really good video tutorial on A1111 by a fellow named Olivio Sarikas.
Hope that helps.

Bit of a warning though, be careful with Git, it wants to install other things, so read the install wizard carefully (Windows Context prompts, an IDE, and Console Window for example), and CivitAI has a nasty habit of softlocking new users if you try signing in with Reddit and Google accounts, just clear your internet Cache.

For future reference of someone who has the same question: You should check free webpages such as Yodayo which are a easier and faster approach, and you can get neat results too.

We have a discord server for information around this: https://discord.gg/furrydiffusion