Bring the sugar, corn syrup, and 1/4 cup water to a boil in a small saucepan. Remove from heat and cool.
Puree the plums, cooled syrup, and lime juice in two batches, using a blender, until smooth. Stir the plum puree and yogurt together in a large mixing bowl.
Pour the mixture into popsicle molds, leaving about 1/2 inch at the top, as the mixture will expand when it freezes. Follow popsicle mold manufacturer's instructions and freeze until solid -- about 4 hours.