Begging gain off small boats.
 

If you target a boat, like the one near Hadden, you can gain begging skill from it.

Can you get money from it?

Lucky you, I can't gain begging skill off of anything. I've gained aggro from things though!

Prime it with a few points and hit it when you walk past animals.

Is it classic? Classically you could get begging skillups from your or another's pet, just never get any coin. Not that you ever got much, if any, coin with even 150+ begging..

I have no idea about boats, but wanted to comment on this.

On live, you could indeed increase begging skill from someone's pet. A caveat to this is that, if that person happened to go LD, the pet would remember you pickpocketing it, and would become aggro. That was a guaranteed iirc.