Muamba suffered a cardiac arrest in the first half of Bolton's FA Cup quarter-final away to Tottenham at White Hart Lane on March 17.
The former England Under-21 international, who turns 24 on Friday, was regarded as "effectively dead" after his heart stopped beating for 78 minutes.
He is now recovering at the London Chest Hospital and last Friday a picture of him smiling was posted on social networking site Twitter.
Coyle, speaking at a news conference on Thursday, said: "He has done some short periods of walking down the corridor he is in as part of the unit, staying in intensive care.
"He is taking steps, talking and has that big smile which we love to see, so he is certainly progressing the right way."
He added: "My chairman Phil Gartside was there yesterday (Wednesday) with our club doctor Jonathan Tobin, and our club chaplain Phil Mason will be there today to continue the support from the football club.
"A couple of players have been sending him messages and we are keeping in touch. It has been great to see that smile and he continues to get better.
"We have to stress that he still has a long way to go, but the improvement has been remarkable and long may that continue."
Meanwhile, Coyle said he hoped Lee Chung-Yong would be back in action before the end of the campaign after the South Korea winger suffered a broken leg in pre-season.
"Lee Chung-yong continues to get better -- he has done some light training on the grass on his own.
"My hope would be - and he needs continued improvement for this -- that he can join in my training with the group in a couple of weeks' time.
"Then, if that is the case, we would need a couple of reserve games and I'd be hopeful that he might be able to be involved before the end of the season."
Bolton, a point above the Premier League relegation zone, are at home to Fulham on Saturday.