Pit the peaches and puree them in a food processor.
Add the coconut cream, maple syrup, and lime juice, and mix in the food processor briefly to combine the flavors. Taste it to see if you want to add a little more syrup.
If you have an ice cream maker, churn the sorbet according to the manufacturer’s instructions, and then place it in an airtight container in the freezer for a couple hours to let the sorbet solidify. I use the KitchenAid Ice Cream Maker Attachment.
If you don’t have an ice cream maker, just put the sorbet directly from the food processor into the freezer.