I just put a Simmons $40 crossbow RedDot on my Winchester 140. Had to spend $13 for an adapter to go from the Winchester grooved receiver to the Simmons 7/8" Weaver mount. Works ok.
A friend put a BSA on a 10-22 last summer and it gave intermittent service. He switched to the Simmons and has good luck SO FAR. We have a special rimfire bowling pin league (pins set on target frame rails rather than a table) and he's got the record of 5 pins in 1.98 sec with that rig. I'm gonna beat him this year.