Is it cheaper to make paper money or coins?

It depends on what cost is being measured.

Paper money is usually cheaper to make than coins because paper, ink, and printing presses cost less than metal and coin presses. For example a US $1 bill costs about 5 or 6 cents to print while it costs a dime or more to make a $1 coin.

But when you look at the whole life cycle of a coin or a bill, coins are almost always cheaper to use than bills. There are several reasons:

• Coins stay in circulation much longer than bills - 30 to 50 years on average, versus 3 to 10 years for bills.
• Worn or damaged coins are easier to dispose of. They can easily be melted down and recycled, while bills have to be specially processed to avoid pollution from the special inks used to print them.
• Coins can be counted reliably by machines, while bills can and do jam mechanical processing machines which requires manual intervention.

It's true that transporting coins is more expensive than bills, and bills are obviously more convenient for large amounts of money. Still, on balance coins remain less expensive than paper money.