What other things aside from a coin that can be tossed or flipped to choose between two alternatives?

Hockey puck
Cookie
Dice
Chicken bones
Card

Cat, although they tend to land heads and tails up at the same time.

Toss a die, having chosen half of the numbers as meaning one or the other alternative, before tossing it.

Of all the platonic solids the icosahedron is the luckiest.

Luck be a lady tonight.

Flip the guy (or gal) that disagrees with you.

@Patty_Melt as to cats always landing heads up, I once heard this:

Cats, when dropped, always land on their feet. And a piece of buttered bread, when dropped, will always land buttered side down. So if we strap buttered bread onto the backs of cats, could we have a new anti-gravity system?

Schroedinger’s cat. Just put it in a box first.

Pancakes

^^Must be tossed pretty high I think.

PANCAKES!!!!!!!!! Yeah!