Coventry boss Coleman, who began his playing career with the Welsh club, had a heroic defensive display to thank for earning a share of their spoils.
Visiting goalkeeper Keiren Westwood made two stunning saves but Coventry's last-ditch rearguard display blunted a Swansea side that have now drawn seven games on the bounce.
In a listless first half, the wind played havoc from the off as Swansea saw a serious of shots blown off target.
Darren Pratley, Alan Tate and Joe Allen all failed to bring their shooting boots as, for all their first-half control, they rarely troubled Westwood in the Coventry goal.
Westwood was called into action with a fine fingertip save to deny fellow Irishman Tom Butler in the 16th minute.
It actually took the Sky Blues until the 34th minute before they finally mustered an attempt on goal, when Freddy Eastwood's low drive was palmed out by Dorus de Vries.
Swansea, whose last victory was way back in November, still looked full of running with their winless streak showing no signs of denting their confidence.
Jordi Gomez's free-kick forced Westwood to make a low save before substitute Gorka Pintado was inches away from netting with his first touch.
Butler went close with a deflected drive in the 66th minute as Coventry continued to soak up the pressure.
But the Swans' dominance could have also been their downfall as they threw bodies forward in the final quarter.
But Wales striker Eastwood missed a golden chance to clinch a late win when a swift breakaway saw him scuff his shot wide with the goal at his mercy.