The Baggies controlled this scrappy derby for long spells but were unable to convert their dominance of possession into a goal.
Jerome Thomas went close to breaking the deadlock in the closing stages of the first half, seeing a 20-yard rocket turned wide before having loud penalty appeals turned away.
Sub Chris Wood could have won it four minutes from time but fired a great chance straight at sub Coventry keeper Dimi Konstantopoulos.
Roberto Di Matteo rang two changes for the club's shortest league trip of the season, with Wood and Marek Cech making way for Robert Koren and Abdoulaye Meite.
With Roman Bednar, Chris Brunt, James Morrison, Ishmael Miller and Neil Clement all missing through injury, the head coach switched to a 4-4-1-1 formation, with Graham Dorrans playing just behind lone striker Luke Moore.
Coventry were hit by the absence of dangerman Leon Best (knee), with Jordan Clarke replacing the six-goal striker in Chris Coleman's only change.
Backed by more than 4,000 fans, Albion steadily settled into their passing stride and recorded the first effort on goal in the seventh minute.
Joe Mattock intercepted a wayward Stephen Wright pass to tee up Moore, who fired straight at Keiren Westwood from 20 yards.
The Sky Blues surged straight upfield and ex-Wolves winger Michael McIndoe came within a whisker of getting on the end of Patrick van Aanholt's dangerous centre.
City suffered an injury setback in the tenth minute when keeper Westwood had to be replaced by Konstantopoulos.
And the sub shot-stopper had to be alert on 14 to race off his line and gather Moore's nod down from Gianni Zuiverloon's diagonal ball before Thomas could pounce.
Just two minutes later, Konstantopoulos had to dive in bravely on the edge of his six-yard box to cut out Koren's low centre, denying Moore the simplest of tap-ins.
Albion were keeping Coventry penned inside their own half but Moore, who had looked lively, was well off target with a 25-yard drive.
City's first real effort on goal did not arrive until the 20th minute when another former Wolves man, Freddie Eastwood, headed well wide form Clinton Morrison's centre.
Back came Albion and Thomas burst through onto Gonzalo Jara's pass, only to see his right-footed drive from an acute angle turned wide by Konstantopoulos' leg.
Jonas Olsson was presented with the game's best chance thus far from Dorrans' ensuing corner but wastefully directed a free header wide from ten yards.
Albion kept knocking on the door and after Thomas was stopped in his tracks inside the box, the ball fell kindly for Dorrans and his right-footed prod from 18 yards looped off a City defender and wide of the right-hand post.
Dorrans' corner was only half-cleared by Coventry and the Scotland Under-21 international was mightily unlucky to see his 18-yard volley from a tight angle fly straight at Konstantopoulos.
The Albion pressure continued when Thomas cut inside McIndoe and unleashed a terrific 20-yard drive on 41.
Konstantopoulos managed to scoop it wide but, in truth, the Greek keeper didn't know too much about it.
The Baggies were enjoying so much possession that Coventry were playing like an away side, although they unable to launch any meaningful counter-attacks.
The half ended on a controversial note when, in the third minute of stoppage time, Thomas appeared to be upended by Martin Cranie inside the penalty area.
Much to the chagrin of Thomas and the Albion bench, referee Keith Stroud booked the ex-Charlton ace for diving!
The second half followed a similar, although much scrappier, pattern.
Sandwiched in between two poor efforts at goal from Olsson and Jara, Zuiverloon intervened in the nick of time at the other end to deny Morrison a simple chance after Albion struggled to clear an aimless long ball.
There was little more in the way of goalscoring chances as the game crept past the 65th-minute mark, although Konstantopoulos once again had to be on his toes to rush out and prevent Moore getting on the end of Koren's throughball.
Coventry recorded their first decent effort for a while on 67 when Isaac Osbourne fizzed a long-range effort two yards wide of Scott Carson's left-hand post.
Albion went agonisingly close in the 73rd minute when sub Filipe Teixeira's deflected shot screwed agonisingly out of the reach of Moore's lunging boot and into Konstantopoulos' sprawling grasp.
The game began to peter out but McIndoe should have done better with an acute 12-yard volley which sailed well wide of Carson's goal.
But it was Albion who should have scored on 86 when Dorrans slotted through sub Wood, with the New Zealand international firing straight at Konstantopoulos.
With that chance went the Baggies' hopes of bagging three deserved points.
COVENTRY (4-4-2): Westwood (Konstantopoulos 10); Cranie, Wright, Turner, Clarke (Bell 69); McIndoe, Cork, Osbourne, van Aanholt; Eastwood (Madine 90), Morrison. Subs not used: Hussey, Ward, Grandison, Cain.
ALBION (4-4-1-1): Carson; Zuiverloon, Meite, Olsson, Mattock; Koren (Teixeira 68), Mulumbu, Jara, Thomas (Cech 83); Dorrans; Moore (Wood 83). Subs not used: Kiely (gk), Reid, Cox, Martis.
BOOKINGS: COVENTRY - van Aanholt (foul 48), Osbourne (foul 55), Cork (foul 90+4). ALBION - Thomas (simulation 45+3), Moore (foul 66), Mulumbu (foul 87).
REFEREE: K Stroud (Hampshire).
ATTENDANCE: 20,871 (Albion fans 4,085).
ALBION STARMAN: Abdoulaye Meite.