Former E.R. star Tierney was forced to pull out of the upcoming series in July (09) after she was diagnosed with the disease, bringing shooting to a halt.
Helen Hunt had been tipped to pick up where Tierney left off, but Graham has been chosen as the star's replacement.
The Bad Santa star will portray a single mother of two teenage kids who moves in with her parents - the same character Tierney played in the pilot episode.
Craig T. Nelson, Dax Shepard and Bonnie Bedelia are also part of the ensemble cast.