Cleverly was due to defend his WBO light-heavyweight title on American soil for the first time, but a contractual dispute between Coyne and former agent Don King has forced the fight to be called off.
Coyne told BBC Wales: "Much as I hate to say it, this fight will not be going forward with myself involved in it. This is the biggest disappointment of my career.
"I trained very, very diligently for this fight and I was devastated when I got the news.
"I want to apologise to the fans in the United Kingdom and the United States that this fight won't be going ahead, but hopefully we can get it on at a later date."
A new opponent for Cleverly could be named later on Wednesday.