Paul and Dominique, whose dad is renowned composer Phil Coulter, moved to New York in December 2010 after he landed a massive solo record deal following on from his four-year stint with classical group Celtic Thunder.
"It's been going on for a couple of months now and the messages have been really nasty. When I came here originally, I was getting loads of fan mail and always always try to reply to them individually. But I was getting these really nasty letters being sent to my PO box in America from this one guy in particular, as well as his sister. They seem to have some sort of vendetta against myself and Dominique," he said.
He initially ignored the negative comments but explained that things then took a more sinister turn when they started targeting both him and Dominique on Twitter.
"One of their tweets said 'America's in an economic recession, go back to Ireland and leave jobs for native Americans. You're not wanted here.' They were slating Dominique calling her a wannabe Paris Hilton and just because she was Phil Coulter's daughter, it didn't give her the right to be here. I came home this week to find her in floods of tears and I just thought, 'enough is enough'."
He promptly reported the abuse to Twitter as well as contacting his local State troopers as he's "taking no chances".
"I just don't want them showing up to any of my gigs and trying to start something there. I don't mind taking the odd bit of abuse but for her to take it is too much so I contacted the police and they're looking into it. It is a form of bullying and I'm not going to tolerate it anymore."
The couple spent Christmas in the States after moving into a property in Sunnyside in New York City. Paul had been touring with male tenor group Celtic Thunder, which scored a string of number one hits in America as well as a sell-out tour. He decided to branch out on his own a year ago. Last month saw him knocking his former band-mates from the top spot with his This Is The Moment album.