After a game has ended, can a player or coach be ejected?

Yes. (OBR 4.01d, 9.01c, FED 10-1-2, 10-2-3c, 10-3-1)

You gotta have strong league backing, though, for the ejection to mean anything.

"You're outta here, coach! And so am I!"

P-Sz

LOL

Perhaps a little more detail on the situation would be appropriate? Otherwise this just sounds silly.

In some (most?) leagues, an ejection carries an extra penalty. Since coaches know this, they sometimes try to hold their anger until after the game, thinking that they are then "safe" from the extra penalty.

Eject them if you can (and it's appropriate, of course), write the report anyway even if you cna't eject. Most (good) leagues will consider that in any penalty.