Muamba was rushed to hospital after collapsing towards the end of the first half of an FA Cup quarter-final away to Tottenham Hotspur on Saturday.
It was later confirmed the 23-year-old had suffered a cardiac arrest and that it took nearly two hours for paramedics to get the midfielder's heart beating by itself again.
Muamba was taken to the London Chest Hospital, just seven miles from Tottenham's White Hart Lane ground, where he remained in a critical condition on Sunday having been anaesthetised in an intensive care unit.
"From our end, and on behalf of the family, we certainly want to say thanks to everybody," Coyle said after visiting Muamba on Sunday.
"Everybody is praying for Fabrice, which is very important, and that has been a real source of strength to the family.
"It's great to be talented at football but it is more important to be a genuinely nice man -- and Fabrice is that. We certainly hope he comes through this.
"Our concern is Fabrice and Fabrice only and that's what all our energy is going into -- hopefully a happy outcome."
Muamba's fiancee, his brother and other relatives have all visited the hospital since his admission.
Bolton chairman Phil Gartside, alongside Coyle on Sunday, said: "The support that we had yesterday from Tottenham and our own fans was fantastic -- the staff, the fans, the players and the officials at the game -- it was unbelievable.
"We have had so many messages of support from around the world."
Following Muamba's on-field collapse, World Cup final referee Howard Webb took the players off the field and then, with the agreement of both clubs, abandoned a tie where the score had stood at 1-1.
Tottenham and England striker Jermain Defoe, who was in tears when seeing Muamba lying on the pitch at White Hart Lane, visited him in hospital on Sunday but, still distressed, made no comment as he left.
Meanwhile Muamba's condition has also led Bolton to postponed their next match, a Premier League game away to Aston Villa due to take place on Tuesday.
As Bolton fans draped scarves and laid flowers outside the northwest side's Reebok Stadium home ground, supporters of other clubs paid tribute to Muamba with a minute's applause before kick-off in several matches on Sunday.
And during Chelsea's 5-2 FA Cup quarter-final win over Leicester, former Bolton defender Gary Cahill lifted his shirt to reveal a "Pray for Muamba" T-shirt after scoring the London club's first goal.
A joint statement issued by Bolton and the hospital shortly after 11am local time (1100GMT) Sunday said: "Fabrice Muamba remains in a critical condition in intensive care in the Heart Attack Centre at The London Chest Hospital.
"He was admitted to the hospital yesterday evening after collapsing at White Hart Lane, where he sustained a cardiac arrest during the FA Cup quarter-final against Tottenham Hotspur.
"Fabrice received prolonged resuscitation at the ground and on route to The London Chest Hospital, where his heart eventually started working.
"As is normal medical practice, Fabrice remains anaesthetised in intensive care and will be for at least 24 hours. His condition continues to be closely monitored by the cardiac specialists at the hospital.
"No further updates are planned at this time," the statement added.
That otherwise seemingly fit players could suffer cardiac problems while playing was brought home to the football world by the death of Cameroon's Marc-Vivien Foe during a Confederations Cup semi-final against Colombia in 2003.
And in 2004, Bolton's Senegal international Khalilou Fadiga, who subsequently recovered, collapsed before a League Cup tie against Tottenham at the Reebok with a heart problem.
Kinshasa-born Muamba moved to England from the Democratic Republic of Congo at the age of 11 after his father fled the war-torn country.
Source: AFP
Source: AFP