It's not common in minis to stand to outside mares, so it'll take quite a bit of work to find one that might. You'll just have to check with mini farms close to you and see if anyone will breed outside mares.
Minis are so small, and if I recall correctly, their sperm doesn't do well with the extender, so AI is rare, if used at all.
I’ve seen a few ads on Craigslist here in TX, but I don’t really pay attention too much since I don’t have any mares. You could try looking on Craigslist or Equinenow or Dreamhorse for horses for sale in your area. Once you find any mini horses for sale in your area, I would contact the owner and ask if they provide stud service or if they know of anyone who does… Doesn’t hurt to ask. Or you could go to a local show and start asking around there. There are usually trainers at the shows who might know of an available stud somewhere in your area. The people I have bought some of my boys from would let me use their stallion if I need stud services, they don’t advertise that though, just word of mouth. So maybe contact the previous owners of your horses and ask them.
Good luck on your search, you’ll have to keep us updated.