I would look on craigslist.com in your area. Make sure you get an older horse, probably 12 and up, calm horse that has been used for lessons and will be very tolerant, caring and gentle with your son. I wouldn't try to break a mini for him. I just bought a 14 year old quarter horse mare for my 5 year old daughter. She is wonderful. She is gentle and takes care of my daughter when she is riding. She was used for lessons ans camps her whole life...thats what you need to look for.
First off, you never want to put a beginner on a newly broke horse, mini or not! Mini's really aren't for riding, you can ride them, but they can only take so much weight. You can get just as hurt by a small horse as you an a large one. I would definitely rule out the mini idea.
Just be very careful, so matter how well broke the owner says a young horse (s) are, when they are young like that, they are not experienced enough to take care of a young, beginner rider.
You can also do a google search and type in : Horses for sale in (your state)
You will get several websites that list horses for sale. Dreamhorse.com is a good one
Just make sure you don't buy a horse going off of the persons word that it is dead broke. Make sure you see the owner ride it before you even consider buying it.
With the horse market the way it is, you may be able to find a fair priced horse that is perfect for what you need!
Good luck!