The 43-year-old, who succeeded the late Gary Speed as Wales manager in January 2012, has come under heavy pressure during his tenure following a raft of poor results.
However, having seen Wales go four games unbeaten, Coleman is confident that the Dragons can qualify for the newly-adapted European Championships in 2016, which will see 24 nations qualify for the tournament in France.
"I believe we'll do it this time," the former Fulham boss told BBC Sport. "I don't say that flippantly. We're in a tough group but I think we've got a good bunch of players.
"We've got the nucleus of a very good team but it's having them together more. You're never going to have them in every game - we just need them for more than what we've had. If we do that then we've got a real good chance.
"We just need them together more often and if we do that and they're playing at their maximum I think we'll have a real successful campaign. Once you've [qualified] once I think that momentum will carry us on and we'll do it again."
Wales are in a group along with Bosnia and Herzegovina, Belgium, Israel, Cyprus and Andorra.