TwoPlayerGames.org offers some free two-player soccer games like 1 on 1 soccer game and Pet Soccer. Silvergames.com also offers some free two-player soccer games like Sports Heads: Football and Big Head Football.
In the 1 on 1 soccer game, both the players have to select their own team from a list of country-level football teams. The pet soccer game is between pets and you can create two different teams having cats and dogs or one can create different teams having a variety of pets.
Sports Heads: Football allows you to choose your favourite soccer player ranging from Wayne Rooney to Lionel Messi and to compete against them. Big Head Football, is a two-player soccer game that allows you to select your personal favourite soccer big head and send him out to defeat all the opponents on the field.