What was made that convinced the Anti-Federalist to support the Constitution?

Answer 1

Federalists promised to add amendments to the Constitution guaranteeing civil liberties. These 10 amendments are what we know now as the Bill of Rights.

Answer 2

The standard answer is "the agreement to add a 'Bill of Rights'" (which, though Madison's masterful management in the House, was accomplished).

But this is actually somewhat misleading. It suggests that all, or at least most Anti-Federalists were supportive as soon as they saw that these amendments were being added. Not really.

In fact, only SOME who opposed the Constitution did so for this reason. Many of them --certainly the biggest ones-- were opposed to the whole SYSTEM laid out in the Constitution (as concentrating too much power in the hands of the central government). None of the amendments satisfied these die-hards. But many of them did, at last at the start, join in the demand for amendments, either hoping that would derail the ratification or open the way for much bigger changes.

What the amendments DID do was satisfy those with 'softer' objections -- and that was enough people that it greatly weakened the Anti-Federalist camp, whose leaders had hoped to force a NEW Convention which would replace the new Constitution with something more to their liking.

I believe some of these folks even OPPOSED the amendments in Congress because they realized they would satisfy enough people to destroy their hope to replace the Constitution.

Now in the end, when the fight was clearly over, these leaders (think of the likes of Patrick Henry of Virginia) came around to support the Constitution -- not to agree with it, but to agree with the system that their countrymen had chosen. A number of these became key leaders in the new 'Republican' party that formed in the 1790s.... a party that worked for a 'weaker' central government, as over against the Federalist party. In other words, they joined the system, even if they didn't think it was the best choice.

In other words, it was NOT the Bill of Rights that made them support the Constitution... it was that the 'fight' was over and they had 'lost'. So they patriotically supported their nation in the path it had chosen.