Despite having beaten Premier League clubs Chelsea (at Stamford Bridge), Fulham, West Brom and Tottenham in cup ties this season, a trip to the Emirates Stadium presents their most difficult challenge.
The Clarets have won many admirers in their cup exploits this season, having lost over two legs to Tottenham in the semi-final of the Carling Cup.
However, Coyle admits it will require more than the attractive football for which they have become known if they are to topple Arsene Wenger's side.
"We know it is going to take a culmination of three things to come together - one for Arsenal to be slightly off their game, two for us to be absolutely outstanding and three a little bit of luck on the day," he said.
"If they come together we have a chance. What you want to do is go and do yourself justice and come off the pitch with no regrets.
"If you have given your very best and it has not been your day I can accept that.
"We have to look to replicate the performances we have shown earlier in the season; if we can do that we have a chance - but I must stress that is all it is.
"Arsenal at the Emirates is a formidable task, and we are huge underdogs on Sunday.
"But everyone loves backing the underdog - and who is to say we can't go there and get a positive result?"
Because of their cup runs, Burnley have played 47 matches so far this season.
However, Coyle is confident his squad - currently seventh in the Championship - will not suffer burn-out as they seek to win promotion to the Premier League.
"I have had a tremendous reaction from this group of players; they want to do the very best for the football club," added the Scot.
"Every time they wear that jersey they do it with immense pride and they show their qualities, and that is what we need to do between now and the
end of the season.
"We have tremendous physical resources in terms of fitness. They have shown they have the mental strength to go with it, and we are going to need all that and a little more on Sunday.
"I think we have character and versatility in abundance, but we also have quality and we have shown that. When all those come together we are a very good side.
"There are no prima donnas - no one who thinks they are above anyone else. It is very much a team effort.
"We have potential match-winners in the team; we have people who can produce a little bit of magic individually. But they bring it within a
team effort, and anything we achieve we achieve as a group."
The Burnley manager predicts their approach to the game will not differ from how they tackle the Championship or the way they faced up to previous Premier League opposition.
"You want to win every game. We are still going on two fronts, being heavily involved at the top end of the Championship also, so we want to continue that," he said.
"We have had a great season up to this point but we can't affect what is behind us.
"But we can affect what is in front of us, and it is important we carry that good work on and are really involved in the business end of the season."
On-loan Rhys Williams is unable to play on Sunday, because parent club Middlesbrough have refused permission for the 20-year-old to feature while they are still involved in the competition. Fellow defender Michael Duff serves a one-match suspension.