The Smith & Wesson 1902 Military & Police (M&P) Model was a hand ehector - the cylinder swings out to the left to load or eject the cartridges. It was built on S&W's K-frame, which today is called the Model 10.
These revolvers were chambered in .32-20 or .38 Special, and the correct cartridge is stamped on the left side of the barrel.
I believe that the correct Vintage stocks would be their size S11, but it might be advisable to e-mail the company for conformation. Their web page is confusing to say the least. Do be sure to also order a screw. Tell them you want stocks for a Smith & Wesson K-frame/Round Butt.
At the time S&W made a smaller frame (the I-frame) which preceeded today's J-frame, which were chambered in .32 S&W Long and .38 S&W (not Special). The stocks for these guns would be too small for the gun you have in mind if we are on the same wave length.
Yes, the stocks were smaller in those days because people often had smaller hands. Keep in mind that larger stocks made for today's K-frame/round butt revolvers will also fit the model 1902 Hand Ejector/Round butt.