The phrase "a difficult time convincing" is correct and usable in written English.
It can be used when describing a situation where someone is struggling to persuade or influence another person.
Example: "I had a difficult time convincing my friend to join me on the trip."
Alternatives: "a hard time persuading" or "trouble convincing".
Regardless of Reeves's role, Capers may have a difficult time convincing McNair to give him another season.
Indeed, luxury companies would have a difficult time convincing all but the wealthiest customers to come into showrooms were it not for lease deals.
Even so, at 5-foot-1, Ms. Page has a difficult time convincing bouncers that she meets the age requirement of 19.
Some insiders say say Mr. Burton may have a difficult time convincing his audience of the real subject of his investigation.
And laying the groundwork is, of course, in his own best interest; otherwise, he's going to have a difficult time convincing the board that his choice is the right choice.
It's usually not a good idea to have the most senior person serve as the leader; she will have a difficult time convincing the others that she is not playing her usual role as boss.
"We think they're going to have a tremendously difficult time convincing anybody that they spent what they claim they spent," Mr. Seyferth said.
But Mr. Meyer and Mr. Valenti have had a more difficult time convincing the studios' Oscar-minded independent subsidiaries to stop mailing the videos.
More generally, people who work in places where conditions are inhospitable and the likelihood that that would have gone to such hostile conditions - if it wasn't for their job - is low will have a very difficult time convincing the IRS that they qualify for FEIE due to the bona fide residence test (but they can still use the physical presence test if they qualify based on days).
Michael Waddels, 57, said that without cameras, the LAPD will have a more difficult time convincing the public that its officers' actions were justified.
HuffPost Sports: Although your female colleagues like Sage welcomed you, did you find yourself having a more difficult time convincing all the guys in the business to respect you?
