Signed by Iain Dowie, Donny was joint top scorer for City Reserves before being told he could find another club with a year left left on his contract.
The forward who came through Charlton's Academy, was loaned to Kilmarmock just before the start of the season and had made 17 appearances for Rugby Park based side, scoring once.
"Donovan is quite happy to stay and Coventry are happy for him to remain here until the end of the season," Killie Boss Jim Jefferies told BBC Sport.
"But he needs the operation as it has been hampering him. It will be a three-week job, hopefully in January. The boy is only 19, but he gives us options."