Neither side could find the net in a largely uninspiring clash at the Oval.
The Glens had Mark Clarke sent-off for a reckless challenge on Ruairi Harkin in the 36th minute of a first half which failed to yield a scoring chance.
Coleraine had the better of the second half and Stephen Lowry fired over the bar when well placed.
Lowry hit the woodwork with another effort while home goalkeeper Elliott Morris made fine saves from a David Ogilby free-kick and Aaron Boyd.
Curtis Allen squandered a late chance and substitute Paul Owens was also off-target late on.
Coleraine lie second in the table on 14 points, trailing leaders Cliftonville on goal difference.
Glentoran drop to third, a point behind the leading duo.