Boil water and sugar in a saucepan over medium-high heat until sugar dissolves. Cool and stir in corn syrup.
Combine chopped plums, 3/4 cup sugar syrup, salt, and allspice in a blender or food processor; process until smooth. Strain mixture over a bowl, pressing to extract juices; discard solids. Combine remaining 3/4 cup sugar syrup, yogurt, and vanilla. Place about 1 1/2 tablespoons plum mixture in each ice pop mold; cover and freeze 30 minutes. Top each serving with about 2 tablespoons yogurt mixture; cover and insert craft sticks. Freeze 30 minutes or until set. Top each serving with about 2 tablespoons plum mixture. Cover and freeze 8 hours or until thoroughly frozen.