Kinzle stated in the comments that it could be Cemetery Man, so I'm posting that as an answer.
Francesco Dellamorte (Rupert Everett) is the cemetery caretaker in the small Italian town of Buffalora. He lives in a ramshackle house on the premises, constantly surrounded by death, with only his mentally handicapped assistant Gnaghi (François Hadji-Lazaro) for company. Young punks in town spread gossip that Dellamorte is impotent. His hobbies are reading outdated telephone directories, in which he crosses out the names of the deceased, and trying to assemble a puzzle shaped like a human skull. Gnaghi can speak only one word: "Gna."
The Latin inscription over the Buffalora Cemetery gate reads RESURRECTURIS ("For those who will rise again"), and indeed, Dellamorte has his hands full. Some people rise from their graves within seven nights following their deaths, as aggressive zombies. Dellamorte destroys these creatures, which he calls "Returners", before they overrun the town. Buffalora's mayor (Stefano Masciarelli) is so fixated on his reelection campaign that he doesn't register Dellamorte's pleas for an investigation. Being an outcast in the village and almost illiterate, Dellamorte doesn't want to lose his job. He opens up to his only friend, Franco, a municipal clerk, but doesn't file the paperwork to get assistance. He explains, "It's easier just to shoot them."
At a funeral, Dellamorte falls in love with the unnamed young widow (Anna Falchi) of a rich, elderly man. She is won over when Dellamorte tells her about the ossuary, which she adores. While consummating their relationship by her husband's grave, the undead husband arises and bites her. She seems to die from the bite, but the coroner claims it was a heart attack. Fearing the worst, Dellamorte stays near her corpse, and shoots her when she rises.
From the TV Tropes page for Creepy Changing Painting:
The old man's headstone portrait in Cemetery Man changes expression from serious (at first) to smug (when Francesco realizes that She is the old guy's widow) to anger (when She and Francesco are having sex on his grave).