Muamba continues to make an encouraging recovery after suffering a cardiac arrest in an FA Cup tie at Tottenham on March 17, and in his absence Bolton have posted successive Premier League wins against Blackburn (2-1) and Wolves (3-2) to boost their bid to avoid relegation.
Asked this morning for an update, Coyle 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.
"My chairman Phil Gartside was there yesterday [Wednesday] with our club doctor Jonathan Tobin, and our club chaplain Phil Mason will be there today [Thursday] 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."
Coyle, who receives the award for a second time, also led Bolton to a 2-1 victory against fellow strugglers QPR on March 10. Bolton's only other league fixture last month ended in 2-0 defeat at title-chasing Manchester City.
"The award is lovely but really it is for the football club," Coyle said. "As much as they call it manager of the month, it is very much a collective effort at our football club.
"The players, staff and fans have been incredible, so on behalf of everybody I'd say we are delighted to pick it up.
"We would certainly love to have April's as well, because if we get that we'll know we have secured ourselves in the Premier League, so that is what we must strive to do in the coming month."
A scheduled league match against Aston Villa on March 20 was postponed following Muamba's collapse.
Meanwhile, Coyle also had news on Muamba's fellow midfielders Stuart Holden and Lee Chung-yong, who have both been long-term absentees this season.
Holden (knee) is back in England after spending some of his rehabilitation time in his native United States, but Coyle stressed the 26-year-old is not expected to make a return to action until next season.
However, the Scot is optimistic that Lee, working his way back to fitness after breaking his leg last summer, may yet feature before the end of the season.
"We are hoping that Stuart will be available for the first day of pre-season training, ready to make that impact that he already has again next year," Coyle said.
"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 are still awaiting clearance from FIFA over their signing of winger Gregg Whyte, who put pen to paper on a three-year deal last month following his voluntary departure from crisis-hit Scottish giants Rangers.
Meanwhile, Swansea's on-loan midfielder Gylfi Sigurdsson has been named the Premier League's Player of the Month.
The 22-year-old Iceland international has been a revelation since arriving at the Liberty Stadium on loan from German side Hoffenheim in January, scoring six goals in 10 appearances, and becomes the first Swansea player to receive the accolade.
Sigurdsson scored both goals in Swansea's 2-0 win at Wigan early on March 3, bagged a brace in the 3-0 victory at Fulham a fortnight later, and was also part of the team that earned an impressive 1-0 win at home to Manchester City.