The Dale slumped to their third successive defeat when they lost 3-2 to Exeter at the weekend and now sit 12th in League Two.
The Spotland faithful have begun to question whether Coleman is the right man for the job following their recent form and slide down the table. He has also received criticism for taking a mid-season trip to Dubai.
But the chairman has offered Coleman his full support and told the Manchester Evening News: "I'm disappointed over recent results, but John remains the man for the job.
"We are three points outside the play-off places just before Christmas for heaven's sake. Certain members of the public seem to have a downer on John Coleman.
"We need to be built solidly for the future and I cannot see anybody who is more suitable for the job than John.
"We were in a bad position last season and we looked for someone to do the job who could handle our sort of budget and our sort of club, and John is the ideal person for that. I believed he was the right man last January and I still stand by that.
"I am disappointed with the last two results and performances, but I think that has become a confidence thing for the players."
When asked about Coleman's holiday, Dunphy said: "I don't feel I was misled in any way. I don't know whether John spoke to (club secretary) Colin Garlick over it, but I was aware he was in Dubai and I've no issues over that."