One of my speaker grilles has come a shade loose and will "buzz" against the door frame when levels are high and certain midbass frequencies are present. (I have aftermarket speakers.) I know it's the grille 'cause I can stop it by putting my hand against the grille -- even light pressure stops it.

What's a good way to tighten this down -- some sort of foam tape? What?

Are you sure it is vibrating against the door panel and not the speaker. There is a circular ring stand out on the inside of the speaker grill which could possibly touch the basket of your speaker.

In any event thin foam tape or the like should do the trick.

I dremeled the inside of the grill to prevent the woofer surround from hitting