There would be several things you could do to convince an Anti-federalist to become a Federalist. During the time when the Articles of Confederation was the plan for our government, we had many issues as a country. Part of the problem was the plan of government was designed to have a weak federal government. This meant the government was very limited in what it could do. This weakness needed to be addressed and was part of the reason for writing a new plan of government.
The Anti-federalists wanted to have a weaker federal government. You could remind them how that wasn't successful in our first plan of government. You could also suggest that the strict interpretation of the Constitution that the Anti-federalists supported would limit what the government could do. This could lead to problems similar to when the Articles of Confederation was our plan of government. The Federalists believed the government should be able to loosely interpret the Constitution. This would give the government more power and a greater ability to deal with issues facing our country. You have plenty of convincing reasons why the Anti-federalists should join the Federalist Party.