Implementing a good connection for pogo pins in eagle
That kind of pogo pin is designed to contact the inside of a plated-through hole. So a hole that takes you about halfway down the cone would make sense. The cone is 1.5mm diameter so a 1.0 to 1.2mm hole, with a pad that at least meets the minimum annular ring specification of your PCB maker. 

There are other variants of probe heads. The serrated head is designed to contact a pad. The concave head goes over a pin or clipped (but not cinched) lead wire. 



This should be fine for testing or programming, however the pressure may not be high enough to ensure long-term reliability if you intend it as a "permanent" connection.