Stir cherries and sugar in a saucepan over medium-high heat until cherries release their juices, reducing heat when they come to a rapid simmer. Maintain a low simmer until cherries are soft and juices start to thicken, about 10 minutes. Cool completely. (Which you can do quickly by scraping the compote into a freezer bag and submerging in an ice bath.)
With an electric mixer (or a strong arm), whisk together cheesecake base ingredients until smooth and fluffy.
In a separate small bowl, stir butter into graham crumbs until it resembles wet sand.
Alternate spoonfuls of cheesecake base and cherry compote into popsicle moulds until about 3/4 full. Top with graham crumble and insert popsicle sticks. Freeze until completely solid, at least 4 hours. To release popsicles easily from moulds, run them under hot water until they come out with a gentle tug.