You would have to pay someone to rebarrel it for you, and I'm not sure what that would cost. Depending on the cost of the barrel and the labor and shop time, that could be almost as much as the gun cost. To my knowledge, Diana has never made the M350 in .20 and the Chinese do not offer a .20cal version of the BAM B28. If they did, I believe you could swap out the barrels. You probably could use the factory M350 spring if you had it converted to .20 cal. .20 cal pellets are in between (weight wise) .177 and .22 so you would not worry about spring fatigue. If you really want a .20 cal, you might look at selling or trading your M350 and buying a rifle that is .20 cal from the factory. The most commom .20 cal guns being from HW/Beeman.
Best Regards
Nathan