i got the same sort of project going and have found the stock i m working with won't stain with normal wood stain and am thinking about trying RIT dye on it ??
Laminated stocks are hard to stain because of the type of wood (birch) and the penetration of the resin into the wood during lamination; that's why the wood is stained before lamination. Dyes work better than stains, I've had pretty good luck with Transtint from Woodcraft; mix it up with alcohol. The other option is to add colorant to the finish.