Some states provide qualified minor parties with their own presidential primaries, and minor parties have used presidential primaries in at least a few states, in all presidential elections starting in 1972.
For 2012, the Green Party seems to be the minor party with the greatest opportunity to use presidential primaries, because it is not nominating a presidential candidate until July. The Green Party is now entitled to its own presidential primary in Arizona, California, District of Columbia, Massachusetts, New York, and West Virginia.
The Libertarian Party has fewer opportunities to use its own presidential primaries, because it is nominating in early May, before primaries are held in many states. However, the Libertarians are free to use presidential primaries in Arizona, Delaware, and Missouri.
The Constitution Party’s national convention is in April, but it is free to use its presidential primary in Missouri, because that primary is on February 7, well before the party’s national convention.
Americans Elect does not wish to participate in any government-sponsored presidential primaries, because it has its own national on-line presidential primary. However, chances are it would be eligible for government presidential primaries in Arizona, California, Delaware, South Dakota, Tennessee, and Utah, and possibly a few other states, if it wished.
Certain other minor parties are eligible for presidential primaries if they wished to use them, but generally they don’t. These include the Conservative, Working Families, and Independence Parties of New York, and the Progressive Party in Vermont. The Peace & Freedom Party always uses its presidential primary in California, as does the American Independent Party in that state.