Whatever you mean by ample line bundle on a DM (say) stack, you cannot of course require that some power of the bundle embeds the stack in projective space. You could ask that some power of the line bundle embeds the stack into a weighted projective stack, but this imposes restrictions on the kinds of stacks you will be talking about. This is studied in a preprint by Abramovich and Hassett where they call such stacks cyclotomic. If you define ampleness in terms of some other positivity (like Kleiman's criterion, Nakai-Moishezon, etc), then you will have many of the same theorems as in the case of varieties - because more or less this positivity will just be "pulled back" from the coarse moduli space. So the answer depends on the situation you are in and the kinds of properties in which you are interested.
mdeland
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