President Trump has been accused by women of rape, however he has never been convicted in court.
If one were to write in a reputable publication that Trump "is a rapist," would such a publication be potentially vulnerable to a libel lawsuit?
It probably would not be, since Trump is a public figure. The ostensibly libeling party would have to act with "actual malice", with "knowledge that the information was false" or that it was published "with reckless disregard of whether it was false or not.
Calling someone a rapist is a factual assertion, so if it is false and does damage to the subject's reputation, it is properly the subject of a defamation action. Of course, the burden of proving whether the assertion is false would fall on Trump. So unless he could prove that he is not a rapist, he would lose his case.
In fact, Trump would have to go even further. Even if it were not literally true that Trump was a rapist, Trump would have to also prove that the "gist" or "sting" of the allegation was false. So even if Trump never had sexual intercourse with a woman who didn't consent, he would also have to prove essentially that he had never engaged in similar behavior. Given his "grab 'em" comments, that may prove impossible. And beyond that, a court would look not only at the single statement that Trump was a rapist, but rather at the full context in which it was made, which may provide additional grounds for ruling against Trump.
The fact that Trump is the president would not change the analysis. But because he's a public figure, his lawsuit would be subject to a higher burden of proof than if he were some random citizen. In addition to proving that he is not a rapist, he would therefore also have to prove that his accuser acted with actual malice, meaning that the accuser either knew that Trump was not a rapist or harbored serious doubts as to whether Trump was a rapist. Given the numerous allegations and Trump's own statements on related matters, it would be remarkably difficult to meet this standard without some sort of admission by the defendant that he seriously doubted his statements.
Nor would it matter whether the statement was made in a reputable publication or in a nonreputable publication. As long as it reached third parties, it could be the subject of a libel action.
So Trump could theoretically prevail on a defamation claim, but he would have to clear all these very high hurdles. Doing so would be exceedingly unlikely.