|By DEJAN KALINIC
The Croatian, who has scored six goals this A-League season, suffered the injury in the first half of Saturday's Melbourne Derby loss to the Victory.
Tadic is likely to avoid surgery and Heart coach John Aloisi hopes to have the 25-year-old back late in the season.
"It is disappointing because Josip has been a class target-man for us and obviously it's not great to lose players of that quality during a run toward the finals series," Aloisi said.
"Fortunately, the extent of the injury is not as severe as we first thought and hopefully Josip will be available for selection in our final three to four matches and beyond."
Former Glory and Sydney FC defender Coyne joins until the end of the season after a stint at Indonesian club Sriwijaya.
The 32-year-old will add much-needed experience to Heart's defence, with Simon Colosimo [calf] absent and Aziz Behich and Michael Marrone having departed overseas.
To add to Heart's injury woes, left-back Sam Mitchinson, 20, is also expected to miss a month with a quadriceps strain.
Mitchinson and Tadic join Colosimo, Fred [quads], Dylan Macallister [adductors] and Mate Dugandzic [foot] on the sidelines.
Irish defender Steven Gray has been released, parting ways by mutual consent.
Heart general manager of football operations John Didulica said the club were planning to make additions to their squad.
"We have opened up a foreign position on the roster so we can hopefully bring in a foreigner to bolster the squad before the transfer window closes," he said."Having added Eli [Babalj] and now Jamie, and with a few guys to come back from injury, we are well-placed to finish the season strongly."