Handrail Fixing problems

[scotty58]

I've taken down the handrail on the stairs which was fixed directly to the wall( outside wall drylined) with the supplied screw fittings. However,on replacing it after decorating,some of the screw holes have literally disintegrated. The screws are 2 1/2" and I think I may have originally used the wrong drill bit and plugs. Has anyone out there any idea which plugs and drill bit I should be using. Would it be better to use a batton on to the wall first ? I'm open to suggestions