Just a tip here.. I use my 39a in smallbore cowboy silhouette competition and always thought it was pretty accurate. When I mounted a scope on it (actually, three over the course of a few weeks) and shot it off my competition benchrest equipment, it wasn't accurate at all, even with $10+ per box of 50 match ammo. After weeks of trying and being ready to either rebarrel the thing or just get rid of it, I stumbled onto the solution. The gun is VERY hold sensitive. If I rested the foreend of the gun on the front rest out near the front end, the gun shot absolutely horrible groups. If I brought the front rest in to right by the receiver, the groups went from 3" or more at 50yds to under an inch. Luckily for me, that's where I support the gun in silhouette matches, which is also why I thought it was accurate from shooting it from matches before.
As has been said, if you stick with lower powers (4 or less), you really shouldn't have much care for parallax as long as you are shooting 10 meters or more with a rimfire. If you move that up to 9 power, you will get some loss of accuracy even as close as 25yds if you use a typical scope designed for a centerfire rifle, because most of those are designed to be parallax free at 100 or even 150yds. That's just the way scopes work, regardless of what any manufacturer tries to say. The only way a scope can be parallax free at all ranges is for it to have no magnification whatsoever. Whether the error induced by parallax is enough for you to care about is another matter, though. No one can make that decision but you. If you are using a 4X scope and need it to be "minute of squirrel head" accurate out to 40 or 50yds, then there's no sense in spending the extra money and dealing with the extra size and weight of an adjustable objective scope (which is how you eliminate parallax and different ranges). That extra cash would be better spent on getting better lenses (inc. their coatings) and a more solid adjustment system.
If you do want a small, adjustable objective scope without spending a ton of money, the Simmons 1022T is excellent for the price ($110 or less on sale). It's a 3-9x32AO with very good lenses and is very small and light. It also should not really be associated with the rest of the Simmons 22Mag line, as they are utter crap compared to the 1022T. To get better quality in a small, lightweight adjustable objective scope, you're probably going to have to spend $250 to $300.