Does anyone have any experience, or recommendations on
an invisible fence system that can be used with a very small
dog?

I don't like the idea of "invisible" fencing, no matter what size the dog. I
know people whose dog has run through the fence to get to something interesting
on the other side; then, after the adrenaline rush was over, the dog couldn't
get back in because the fence kept him out. Also, an invisible fence, even if
it keeps your dog in, can't keep other animals (or humans with evil intentions)
out. This leaves your dog vulnerable to attack or theft. If you can't put up
a "real" fence, I would suggest that you either bring your dog to a securely
fenced dog park to allow off-leash fun, or use an overhead line with a leash
attached so your dog can run (with you in the yard supervising, of course)
JMHO
Dorothy, owned by C.C., a very spoiled dachshund