Can I still crown a king if I run out of pieces?
(Warning: Clicking on the rulebook link below will download a Word document.)

From the American Checkers Federation's official rulebook (emphasis mine):


  1.16  When a man reaches the farthest row forward (known as the “king-row” or “crown-head”) it becomes a king, and this completes the turn of play. The man can be crowned by either player ( ) by placing a man of the same colour on top of it before the next move is made. (It may be necessary to borrow from another set if no captured man is available for the purpose). 


Like the rules say, if you run out of pieces, you can just borrow from another set. You are not limited by the number of pieces in your set.

If you are playing casually with friends, you can crown a king using coins, dice, torn pieces of paper, etc. As long as the board state is clear to you and your friends, it doesn't really matter how you crown your kings.