I've used General Finishes Dye stains with good success. They're alcohol based, come in a red label can. The names of the colors are basic as heck, "light brown" and "dark brown" for instance, versus their water or oil base stains that are descriptive names like "silk grey" and stuff.
when I've used them I wiped on lightly after final sanding to thickness, then wiped off. If your veneers or core lams are too thin or figured, they'll curl when they dry. I then let them sit 48 hours prior to gluing so I know it's dry. I think the oldest bow I've done with that method is 1.5 yr and probably 15,000 shots? The guy that has it shoots a TON.