The answer is one half-dollar and one nickel. Usually the riddle is written How do you make 55 cents with 2 coins where 1 is not a nickel. The trick is the other one is a nickel.
United States dollar
Liberty Head nickel
The Shield nickel was the first United States five-cent piece to be made out of copper-nickel, the same alloy of which American nickels are struck today. Designed by James B. Longacre, the coin was issued from 1866 until 1883, when it was replaced by the Liberty Head nickel. The coin takes its name from the motif on its obverse, and was the first five-cent coin referred to as a "nickel"—silver pieces of that denomination had been known as half dimes.
Silver half dimes had been struck from the early days of the United States Mint in the late 18th century. Those disappeared from circulation, along with most other coins, in the economic turmoil of the Civil War. In 1864, the Mint successfully introduced low-denomination coins, whose intrinsic worth did not approach their face value. Industrialist Joseph Wharton advocated coins containing nickel—a metal in which he had significant financial interests. When the Mint proposed a copper-nickel five-cent piece, Congress required that the coin be heavier than the Mint had suggested, allowing Wharton to sell more of the metal to the government.
Coins of the United States
The Liberty Head nickel, sometimes referred to as the V nickel because of its reverse (or tails) design, was an American five-cent piece. It was struck for circulation from 1883 until 1912, with at least five pieces being surreptitiously struck dated 1913.
The original copper–nickel five-cent piece, the Shield nickel, had longstanding production problems, and in the early 1880s, the United States Mint was looking to replace it. Mint Chief Engraver Charles Barber was instructed to prepare designs for proposed one-, three-, and five-cent pieces, which were to bear similar designs. Only the new five-cent piece was approved, and went into production in 1883. For almost thirty years large quantities of coin of this design were produced to meet commercial demand, especially as coin-operated machines became increasingly popular.
Coins of the United States dollar were first minted in 1792. New coins have been produced annually since then and they make up a valuable aspect of the United States currency system. Today, circulating coins exist in denominations of 1¢ (i.e. 1 cent or $0.01), 5¢, 10¢, 25¢, 50¢, and $1.00. Also minted are bullion (including gold, silver and platinum) and commemorative coins. All of these are produced by the United States Mint. The coins are then sold to Federal Reserve Banks which in turn are responsible for putting coins into circulation and withdrawing them as demanded by the country's economy.
Today four mints operate in the United States producing billions of coins each year. The main mint is the Philadelphia Mint, which produces circulating coinage, mint sets and some commemorative coins. The Denver Mint also produces circulating coinage, mint sets and commemoratives. The San Francisco Mint produces regular and silver proof coinage, and produced circulating coinage until the 1970s. The West Point Mint produces bullion coinage (including proofs). Philadelphia and Denver produce the dies used at all of the mints. The proof and mint sets are manufactured each year and contain examples of all of the year's circulating coins.