The Australian is one of 14 members of the International Olympic Committee Executive Board who voted in Lausanne to recommend wrestling be dropped from the Games after 2016. The board's 15th member, IOC President Jacques Rogge, did not vote.
Wrestling featured in the first modern Games in 1896, and in all but one of the subsequent editions, and the decision prompted uproar around the sporting world.
Coates, however, thinks wrestling will be on the shortlist after the board meets in St Petersburg in May to decide which of eight candidate sports will proceed to the next stage.
The shortlisted sports will face a vote of the full IOC for one place in the 2020 Games in September in Buenos Aires, where Coates believes the wider electorate will favour wrestling.
"I would be very surprised if wrestling isn't one of those (on the shortlist) and you could well get a very different result when there's 115 people voting as opposed to 14," he said.
"So all we've done is a recommendation. My guess is, the one that will find it most difficult because of the groundswell of support for wrestling is going to be the baseball-softball combination, because both those sports and wrestling very much depend on the Americas."
Baseball and softball have joined together in a bid to return to the Games, while squash, karate, wakeboarding, roller sports, sports climbing and wushu are the six other candidates for inclusion.
Baseball and softball were dropped from the Olympic programme after an IOC vote in 2005 and were last played at the 2008 Beijing Games.
The growndswell of support for wrestling includes the ANOC chief Sheikh Ahmad Al-Fahad Al-Sabah, who said on Tuesday that his executive committee unanimously backed retaining the sport.
"We are very keen to maintain wrestling in the sport programme," he told Australian Associated Press.
"Like everybody we're surprised wrestling is out of the programme ... I think there's surprise not only in this house, but outside. Even in the house of the IOC when the result was announced. Surprise was everywhere.
"We will work very closely with the wrestling (federation) and the NOCs and the continent organisations to give us support for wrestling to maintain its place in the sports programme."
The vote to recommend the ousting of wrestling had lessons for all sports, and wrestling needed to learn quickly if it was to survive, said Coates.
"I was amazed the way it all went ... in the last vote it was eight against wrestling, three against hockey and three against modern pentathlon," he recalled.
"Clearly modern pentathlon has done much to reinvent itself in recent times. Perhaps wrestling needs to do more in terms of more women's events, their governance."
- Sports & Recreation