If the stock's loose on this little .22 pump and you've tightened the screw on the frame as much as you can, what next? How do you "fix it right", or is it just supposed to have give or side to side wobble in it?

Couple ways to go. Could glue in some wood and refit. Or could use some AcraGlas.

Try another washer under the head of the stock screw, there is a chance that the threads are bottoming out before the stock is tight.

Thanks guys!

It should fit tight even w/o the screw in place.

Check to see if one of the 'ears' / side panels of the stock is cracked even just a bit along the tang inletting. That relieves the pressure of the fit and can allow side to side wobble. Especially when the screw isn't tightening up correctly.

If the tang screw hole is over size (or the wrong tang screw), it'll allow the entire action to pull forward a bit & let it move around. Using it that way makes the fit worse as time goes on.
Combined w/the above, it can make for a very loose action to wood fit.

The Model 62 actually had the flat mainspring of the Model 90 pump and used the same stock and inlet.
The 62A changed to a coil mainspring set up and required a slightly different inlet IIRC.

I'm not sure a 62/90 stock will go right on a Model 62A w/o some tinkering with the inlet for the coil spring.

All fixable with some time and AcraGlas as stated above.