When did they stop making silver coins?

Actually most modern U.S. coins are almost entirely copper. Nickels are 75% copper; dimes, quarters, and halves are 92% copper, and dollars are 88.5% copper (source: U.S. Mint).

The only coin that's NOT mostly copper is the penny. Starting in mid-1982 the coin's composition was changed to a core of 97.5% zinc with a plating of 2.5% copper.