Rather than do a full-blown accent, I think most singers are well-off to use a "lilt" that reminds the listener of the song's intended accent. And I think most people can pull that off pretty well, if they don't try too hard or get too fussy about it.

I know a rather attractive American woman who can turn on her Irish lilt anytime she wants. And every time she does it, I'm smitten.

-Joe-