Shona Auerbach’s heartfelt melodrama may rely overmuch on manipulative artifice, but there are plenty of rewards at the end of this bittersweet rainbow. The title refers to the opening salutation of the letters that Lizzie (Emily Mortimer) pens to her deaf nine-year-old son (Jack McElhone). The catch is that the letters are supposed to be from his father, whom Frankie hasn’t seen since he was a bantling. The story Lizzie has cooked up is that dad is out at sea toiling on a freighter, but the reality is that he’s an oddball with an unsavory disposition who pursues her from afar. One day, the ship that he’s supposed to be on sails into port, and Lizzie is pressed to find a surrogate (Gerard Butler). McElhone’s subtle, physical emoting and Auerbach’s loving depiction of a damp, glum Glasgow help lift the film above its treacly underpinnings, and Sharon Small (Havers on PBS’s Inspector Lynley Mysteries), as the shopkeeper who brokers the father-for-hire deal, adds a shot of vigor. (105 minutes)