2 tips that work for me:
I don't bother draining the coolant first. I just loosen the pump bolts without removing them and crack the pump off of the block. All of the coolant quickly drains directly from the block. Once it has finsihed draining, I fully remove the pump. It's a little crude, but it works.
When I refill the system, I pull the thermostat housing and pour the coolant directly into the engine block. I usually replace the thermostat when I replace the pump, so I have the housing off anyway.