I agree with Assassin, the 22LR barrel can be reamed and throated for the 22 Mag, but you can't shoot 22 LR in it any longer. I tried doing that and had the case broke up in the chamber.
I prefer the Contenders in 22 Mag over the 22 LR, the Mag is a better hunting caliber and in the modified Contender they are very accurate. If you are not doing the work yourself and don't own the equipment to rechamber the Contender, you may be better off looking for a 22 Mag barrel. It isn't that simple to do it right.
Jerry