I believe it may be possible to repair this problem. My first concern is what type of play you have and how much? Is the barrel moving forward? primarily wobbling up and down? or both. If the gun is still firing, it will more than likely just effect accuracy. If it gets worse you may experience a fail to fire situation or at the worst case scenario a split case after firing.
I guess you are probably just suffering a loss in accuracy and don't need to worry about a split case all that much.
If you purchased the gun new or it is "newer" contact Marlin, It may be under warranty and they might repair such a problem free of charge. (minus shipping)
If you need to repair it yourself, you will need to find out where the play is coming from. Most .22s I have played around with usually have a "tolerance fit" between the barrel and receiver meaning that the just slide into the receiver with some friction and then pinned or bolted to keep them from moving rather than threaded in like conventional centerfire barrels.. I have a Glenfield model 60 (same) here that is just a barreled action at the moment and I could not see whether or not it was threaded. I looked at the schematics
(great company I have spent thousands of dollars with them with only one small problem not worthy of mention) and it appears that it is a "tolerance fit" Bbl. as well. I did not pull my barrel to find out.
Without experiencing your problem with you. I can only figure on three causes of play. The amount of space between the part of the barrel that touches the receiver, the spaces around the pin or both. The pin contacts the receiver on both sides as well as the barrel. Space between the barrel and receiver would cause a wobbly type of play. The pin would allow more of a forward-backward movement.
I agree with roklok. For repairing excessive space between the barrel receiver it should work okay. Acraglass has some elasticity, but so does the receiver and barrel so I don't think you would need to add steel or brass powder to it. I think black loctite would work to. I am more familiar with acraglass and found that if you make a boo boo. a small amount
of heat will usually help get it loose again. If you go this route, you will need to pay attention to the two angled slots ot the side of the barrel. They are for the extractors. Clog these slots and you will have problems. Also try and keep the barrel strait. I worked on an old savage a while back. Where play was bad enough to cause everything to move resulting in a fail to fire. This was caused by a warped stock and poor maintenance (left outdoors all of the time) and not related, but just a good idea.
As far as a pin problem goes. I need to know what its doing. May just need a new or slightly bigger pin.
Let me know if I can be any extra help.