There are several ways to do it, but if you can't figure out the right blending mode one simple way would be to disable alpha writes: al_set_render_state(ALLEGRO_WRITE_MASK_FLAGS, ALLEGRO_MASK_RGB)
I tried drawing a tinted bitmap, but the image is mostly black so I don't think it works because there isn't color to tint. Also, for some reason it seems like al_set_render_state() is nowhere to be found.
You mean your version of Allegro doesn't have al_set_render_state?
What do I have to include to use it? I can't really find information on it anywhere.