I am not sure why you would stain a metal door either. And as far as
the metal primers go on these doors, any of them will "accept" an
opaque stain. The opaque stains are little more (yes, I know the
actual composition and colorants vary some) than thin paint that has
different solild compositions.
Find a real paint store like Benjamin Moore, Sherwyn Williams, or any
other honest to Pete paint store, not HD or Lowe's, and get their
color charts. Different manufacturers use different color charts for
metal paint, but there are lots of different colors you can get. Not
as many as in a latex color deck, but still a surprising amount.
Buy metal paint, put on a couple of coats and you should get years out
of the finish if properly applied.