Small footprint reference design to charge a capacitor using LTC4124

For a project with a tiny PCB (12mm diameter) we want to charge a 470 uF capacitor at 4V. The maximum charge rating for the capacitor is 50 mA. With the capacitor we power a BLE IC (1.8-4V 5 uA). 

On your site we noticed a simple charging circuit for a Li-Ion battery, is there a reference design for this to be found? How would we need to adjust it to power this capacitor instead?

Hope to be in contact with anyone who has tried this before and/or an Analog Support Engineer.