Freddy Eastwood had given City an 18th minute lead but the Scot landed his team a share of the spoils from the spot.
Both teams exchanged blows early on with Coventry's Michael McIndoe forcing a save from Andy Lonergan before Keith Treacy beat Leon Barnett but he saw his low effort stopped by Keiren Westwood.
The home side opened the scoring as they broke clear after a Preston attack. David Bell's cross found its way to McIndoe who waited for a second before passing to Eastwood ten-yards from goal and the striker calmly rounded Billy Jones before firing low into the net.
Ross Wallace forced a couple of saves from Westwood from long-range before the Sky Blues conceded a penalty.
Jon Parkin got in between two defenders on the Preston right and was upended by Richard Wood and referee Gavin Ward adjudged it to be inside the box.
Davidson stepped up and fired the spot-kick home to draw Preston level after 35 minutes.
Clinton Morrison went close just before half-time when he turned in the box but volleyed straight at Lonergan.
Davidson almost doubled his personal tally straight after the break but fired wide before Parkin headed over after shrugging off Stephen Wright's challenge at the back post.
Wright then set up David Bell at the other end but his low shot was well wide of Lonergan's left-hand post.
Parkin had a chance in the 80th minute after bringing the ball down on his chest but his fierce effort was saved by Westwood once again.
There were five minutes of added time but neither side came close to winning it and the points were shared at Ricoh Arena.