Correct - Coyle turned us around after Clark/Stark took us backwards and Connolly sunk us completely. Coyle brought in some solid pros for us, brought back a feel good factor and an identity to our team and started our upward trajectory. We went from 8th to 2nd in his first full season, finished 1 point behind Gretna (who scored in the 93rd minute of their match - arguably the best thing that could have happened to us in the long term, but that's a point for another thread) and then started slowly the following season before he left for Burnley. Should be remembered that he also brought in McInnes, who took us up and carried on what Coyle started.
Coyle left us at the right time - I felt at the time he was running out of ideas, although we did improve in the final month or so of his tenure - but he'll always be fondly remembered by Saints fans for starting the best period in our history after a desperately poor few years before.
He's had a patchy record since Bolton but I think he'd do a great job for Falkirk if he ends up taking the job on.