Teacher of sports would be sports' (not sport's) teacher, but an apostrophe is nonsense there anyway.
Naturally I am a big fan of the apostrophe and keep a felt tip pen in my golf bag to add, and renew (after heavy rain), the apostrophe on the Captain's Bunker sign.
I implored management to put TROLLEYS next time they renew the several 'No trollies or buggies' signs. They've just put up new ones exactly the same.