I think you are going to have a tough time finding one for that cost, most of the ones I have seen from various brands are in the $150 up to $300 range.
Bushnell makes the firefly that is a nice scope for a .22 but it is out of your range.
Here's a BSA at Cabella's but magnification is less than you want, cost is more and finally and certainly not least it's a BSA. You will get what you pay for and that's not much. Personally I think you should drop the illuminated reticle requirement and you could get a fairly decent Simmons at your price point. They have a 3-9x50 there for $80 but I don't know if you could even get it on a .22.
Simmons makes a 3-9X32 with A/O in it's .22 Mag line. I see them going for under $100. I bought one, and it's a good scope. Not as bright as a Leupold, but it works fine on my 10/22. Adjustments are reliable, and repeatable, the A/O is close to perfect, and I paid $70.00 for it. One of the new Master Series scopes.
I found a few of the Barska scopes from sportsmansguide for $44.97 I might look at buying but I will probably just save my money and buy a good quality one to begin with.