Display Tags Meta-Box on my own plugin page?

So, I’m writing a plugin which, at one point, creates a new Post.

What I want is to display Tags meta box (the one found in New Post), to allow user to choose tags for it.
The main reason I want “that one” (and not just a textbox with comma-separated keywords) is obviously to have the Ajax-dropdown suggestion list.

add_meta_box() works only with Write Post, Write Page, and Write Link pages.

I’ve tried something with do_action() but with no luck.
I can always use plain textbox, but this would be much better.

Any ideas?