No, a recount has never lead to a change in the outcome of a state in the US presidential election. I will go into two specific cases where there might be some doubt. I don't think there are any other cases where there is doubt a recount changed the outcome of the presidential election in that state.
Florida, 2000
In 2000, the following happened in Florida, according to the New York Times:
In 2000, Gov. George W. Bush of Texas and Vice President Al Gore were statistically tied in Florida, and the state’s electoral votes would determine the next president. The U.S. Supreme Court ended the state’s recount, however, on the grounds that the Florida Supreme Court, in failing to set counting standards that would treat all voters uniformly, violated the Equal Protection Clause of the 14th Amendment.
So the recount didn't change the outcome.
Florida, Louisiana and South Carolina, 1876
The election was disputed in 1876, but there was no recount.
According to Politico:
A far more serious crisis unfolded in 1876, and this is one that may indeed have swung the election the wrong way, depending how one interprets the historical record (a topic I have taken up elsewhere). Preliminary returns showed the Democrat, Samuel Tilden, winning Florida, Louisiana and South Carolina—any one of which would have been enough for him to win the Electoral College—and thus the White House. But his opponent, Rutherford B. Hayes, did not concede on Election Night. Instead, word went out from the Republican Party’s national headquarters to local partisans in all three of these states: If Hayes captured all three of these states, the GOP’s telegram said, then he rather than Tilden would achieve an Electoral College victory. Republicans on the ground in these states indeed managed to convert an apparent Tilden victory into a Hayes victory through control of each state’s canvassing board. When Congress, after a tortured process, confirmed each state’s newly certified returns in favor of Hayes, Tilden was the one who was eventually required to concede, which he begrudgingly did.
A number of states ended up sending competing slates of electors, according to the New York Times:
With the future of Reconstruction on the ballot, the presidential election of 1876 was hard fought. Tilden decisively defeated Hayes in the popular vote by about 250,000 votes, but in four states — Florida, Louisiana, Oregon, and South Carolina — both parties claimed to have won electoral votes. At that point, Tilden needed only one more electoral vote to win, so any of the four would suffice.
However, Republicans still controlled the election canvassing boards and governorships in the three southern states, which led to the manipulation of vote counts and the subsequent awarding of electoral votes to Hayes. Democrats refused to give up and sent competing slates of electors for Florida, Louisiana and South Carolina to Congress. In addition, the Democrats challenged the eligibility of one of Oregon’s electors, a fail-safe that would lead to a Tilden win even if Hayes claimed victory in the three Southern states.
Eventually, the election was settled in the Compromise of 1877:
The Compromise of 1877 was an unwritten deal, informally arranged among U.S. Congressmen, that settled the intensely disputed 1876 presidential election. It resulted in the United States federal government pulling the last troops out of the South, and formally ending the Reconstruction Era. Through the Compromise, Republican Rutherford B. Hayes was awarded the White House over Democrat Samuel J. Tilden on the understanding that Hayes would remove the federal troops whose support was essential for the survival of Republican state governments in South Carolina, Florida and Louisiana.
Again, the election was disputed, but it was resolved through compromise. As far as I can tell, there was no recount in any of those four states.
