Adams wasn't as poorly regarded in his day as history makes it out to be. He made some pretty big mistakes, but the fault was as much Hamilton's as his. The Federalists actually made their highwater mark in 1798 (60 of 106 seats in the House, 22 of 33 seats in the Senate). The XYZ affair of 1797 had turned public opinion ran strongly against the French. The Quasi-War was actually quite popular with the majority. The Federalists took advantage by preparing for an invasion by the French Army, creating a navy and a standing army. The taxes that paid for this were unpopular with some segments of the population, but not debilitatingly so. Same goes for the Alien and Sedition Acts.
Things really went wrong because the key driver behind all of this was Hamilton. Adams tried to free himself from Hamilton's overbearing influence in early 1799, and did so by unilaterally sending overtures of peace to France. This divided the federalists between his supporters and Hamilton's. Adams fired Hamilton's group from his cabinet. Hamilton then became deeply embittered, wrote scathing criticisms of Adams, and started conspiring to undermine Adams and throw the 1800 election to Charles Cotesworth Pinckney.
No Alien and Sedition Acts is probably a plus, and building a navy but no (or just a nominal) standing army would probably be wiser than what they did. Most importantly, the internal struggle must be avoided, and Adams must certainly not open peace talks with France in order to spite Hamilton. The best POD, then, is simple: Hamilton gets run over by a carriage in early 1798. His absence results in the above changes, the public support for the Federalists remains strong, and Adams wins in 1800.