The Frenchman was confirmed as Jason Kreis's successor at the MLS side, and will leave his role as the head of Manchester City's Elite Development Squad to take up the position with the franchise on January 1 to build his side for the new campaign.
Coyle believes that Vieira has all the tools at the club to have success, but will have to endure the trials and tribulations of football management just like everyone else.
"I don't think it's down to me to give him advice," Coyle told Sky Sports News. "But Patrick is such an honourable figure, he's an outstanding player.
"He's been working at Manchester City, and [sporting director] Claudio Reyna is there as well, so Claudio will be able to help him on that route.
"I would say that as much as the team will give him all the bits and pieces, nothing will beat the experience of actually learning on the job and it's a tough environment."