This is a common job for practicing gunsmiths.
When you cut the stock you will find that it is either hollow or filled with a lightweight material like foam. What you need to do is figure out exactly how you want to install the new pad.
The best jobs are done by those who take the time to fit a piece of hardwood into the hollow butt and then install a pad in the conventional manner using the wood to hold the screws.
A quicker, not as strong, (and to my mind slovenly) job can be done by using an adhesive to attach the pad. The biggest problem with this type of work is that the difference in flexablity between the stock, the pad, and the adhesive allows failure after a short time.