The Football Association upheld Wanderers' appeal against England defender Cahill's controversial sending-off in Saturday's 3-0 Barclays Premier League defeat at White Hart Lane.
The defender therefore escaped a one-match ban, allowing him to face former club Aston Villa this weekend in a match Bolton must win to stand any chance of climbing out of the bottom three.
Coyle was confident Cahill's appeal would not fail, telling the Bolton News: "You can never be 100% about anything. But we were confident that this would be the outcome.
"Hopefully, that's the end of this run of bad luck we've been on, with suspensions and everything else. These things are sent to test us. We've played huge chunks of three of the last five games with 10 men and that has been difficult. But, as far as I'm concerned, the time for talking has got to stop. We have to start picking up points.
"That starts on Saturday against Aston Villa, heading into a run of games where I think we can start moving up the table and out of a position we don't want to be in."