Pulse drained cherries in a food processor until chopped. Transfer to a large bowl. Add yogurt, evaporated milk, sugar, half-and-half, milk, and creme de cassis liqueur; mix well.
Pour into an electric mixer's ice cream attachment. Follow manufacturer's instructions and mix for 25 minutes on the 'stir' setting.
Pour the chilled mixture into a freeze-proof container and freeze until it reaches "soft-serve" consistency, about 2 hours. Transfer frozen yogurt to a one- or two-quart lidded plastic container; cover surface with plastic wrap and seal.