Drain pineapple, reserving 1 2/3 cups pineapple juice.
Combine pineapple juice, sugar, and syrup in a large Dutch oven. Bring to a boil, stirring constantly. Cook over medium heat, without stirring, until mixture reaches soft ball stage (234°). Add reserved pineapple slices; return syrup mixture to a boil. Reduce heat; simmer 20 minutes or until pineapple is translucent. Carefully remove pineapple with a fork, and drain on wire racks.
Add cherries to syrup, and return to a boil. Reduce heat; simmer 20 minutes, stirring occasionally. Remove cherries, and drain on wire racks. Let fruit dry on racks 24 hours. Store in airtight containers, or freeze.