What kind of stock do you have? Wood? Composite?
What you are talking about doing is kind of, well, kind of hokey to be honest, but it will serve the purpose...
All you are needing to do is order a 1913 Picatinny Rail, in whatever length you want, then get a couple of screws and a couple of nuts.
Take the stock off the gun. Measure, mark and drill a couple of holes into the stock that coincide with the holes in the rail.
Turn the stock over and countersink the holes under the barrel so they don't have the nutss, or the screws, adding pressure to the barrel.
Drop the nuts in the countersunk holes, thread the screws in from the bottom with the rail in place, trim screw length as needed.
A little Locktite, or clear fingernail polish, and you are good to go.
It's not like you are adding a scope rail to a 1,000 yard gun....