Can't Buy Me a Duke - The Duke Hunters Club, #7

When a reclusive American heiress learns her younger sister is forbidden to get engaged until someone courts her, she pays a duke to pretend to be her suitor. Lucy Banks will never be mistaken for the belle of the ball. Her red hair, freckles, and reputation for surliness make that impossible, no matter how much money her father earned in Manhattan. Unfortunately, her parents didn't move across the Atlantic so Lucy could struggle to find a husband.
Even more unfortunately, her younger sister cannot have a suitor until Lucy's future is secure. Unless Lucy can find someone to court her, she is standing in the way of her sister's happiness. Fortunately, Lucy is willing to pay. Harrison James, Duke of Sturbridge, might be beloved by the ton, but he has no intentions of ever marrying. That would mean exposing a bride to his secret, and that is impossible. When Lucy offers him money to feign romantic interest in her, he reluctantly agrees.
Once Lucy returns to New York, he can pronounce himself brokenhearted and avoid another year of questions. Lucy and the duke now only have one problem: they must not confuse their hearts with their fake courtship.