Assuming the rifle is a Carcano, converting to 6.5x55 is theoretically possible but not feasible. Not only would the bolt have to be changed (and there is not a lot of room, but the magazine would have to be both lengthened and widened. I doubt the conversion could use the original clip system; the clips simply could not be widened, you would need to make new clips, which would not be feasible.
Converting the magazine to avoid use of a clip (which was done with the German 1888 Commission rifles) would be very costly.
In other words, unless you have lots of money and want to do something just to prove it can be done, your best bet is to keep checking for 6.5x52 brass that can be reloaded.
Jim