I'd recommend setting up local installation if your PC is at least decent. KoboldCPP as backend, Silly Tavern as frontend.
It's secure, private and free (excluding electricity costs). To be honest, quite user-friendly too despite what you might think.
Some good lightweight models I tried (and you can find at huggingface): NemoMix-Unleashed-12B; NemoReRemix-12B, L3-8B-sunfall. If you manage to set up it and run, you can go higher and I do not want to recommend particular models, as they are ever-evolving.
To find character cards for Silly Tavern, use chub.ai. I did find some cards focusing on spanking, unfortunately most by anonymous authors, for example:
https://www.chub.ai/characters/Anony...p-a746001bc9c4
But honestly, most scenarios can easily be modified to focus on some form of spankings.
You also can set up Tavern to run Kobold CPP from your other PC or service like openrouter (gets too expensive pretty fast)