Both sides went into the game looking to end recent bad form but neither did enough to justify winning the match.
Coventry started brightly and Clinton Morrison put two early crosses into the box, but on both occasions the ball was out of Freddy Eastwood's reach.
In the ninth minute, the home side had their best chance of the half. Patrick van Aanholt received the ball on the left and sent a great delivery to the back post. Michael McIndoe ran onto the cross but couldn't turn the ball into the net from close range.
The Sky Blues suffered a blow a minute later when goalkeeper Keiren Westwood was replaced, with Dimi Konstantopoulos taking his place.
West Brom started to come into the game, with much of their attacking threat coming through winger Jerome Thomas. He managed to beat Martin Cranie in the 27th minute, but his shot bounced off the outside of the post and wide.
Konstantopoulos was then called into action twice in a matter of minutes to deny the Baggies the lead.
First, Graham Dorrans smashed a half-volley towards goal after a half-cleared corner - but the Greek keeper managed to gather the ball well. Then he was forced to tip a Luke Moore low blast wide.
The second half was more defensive and it took more than 20 minutes for an attempt on goal, when Isaac Osbourne hit a 30-yard shot over the bar.
The later stages of the game were a slight improvement, thanks partly to the introduction of Filipe Teixeira.
In the 73rd minute, his dribble and resulting shot deflected off a City defender and was inches away from falling to Moore.
Chris Wood then went close in the 87th minute, after Dorrans' throughball. The substitute was one-on-one with Konstantopoulos, but the keeper blocked well to give Coventry their first clean sheet in 11 games.