Mounting scope securely on 1950's mod.317 Benjamin "Franklin"

[BJPumpman]

I've been trying to mount a scope on the barrel of my old 317. I had the gun seals etc. replaced several years ago and recently broke down, cleaned and rebuilt the whole gun. Bought scope mounts and a decent 4x scope from Pyramid air. Most of the gun including the barrel is brass. The problem is that apparently, the older brass barrel has a smaller diameter than the newer models and I cannot get the scope mounts that clamp around the barrel tight enough to hold the scope in place. I've tried two mount models. I can shim it but don't know what material would be best. Anyone know how to resolve this short of buying a newer model. Come to think about it, I've always wanted a .20 cal.