Coffey, who missed the second half of the season after undergoing his second Tommy John elbow reconstruction surgery, was bought out of a $2.5 million salary for $300,000.
Rivera, who shuttled between left field and first base until the trades for Shane Victorino and Adrian Gonzalez, was bought out of a $4 million salary for $500,000.
Treanor, who saw only sporadic action backing up A.J. Ellis, was bought out of a $950,000 salary for $150,000.
The Dodgers have seven players eligible for free agency -- Bobby Abreu, Joe Blanton, Randy Choate, Adam Kennedy, Brandon League, Victorino and Jamey Wright.
General manager Ned Colletti said he wants to re-sign the three relievers -- League, Choate and Wright. League is the highest priority and could be the first deal done.
Ken Gurnick is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.