Take the worst one apart and find out what is wrong. Just looking at the outside, it appears that the crank runs a pinion that engages a rack attached to a piston. The piston would run up and down in the cylinder of the pump.
To operate, you crank on the handle, raising the piston until it stops. That should be one unit (pint or quart probably), and then reverse the crank to lower the piston. Repeat until the desired amount has been pumped.
There will be a packing around the piston, a packing around the operating rack, a packing on the crank handle, and a couple of one-way valves. As old as those are, I doubt that the packings will be fancy, so you should be able to make something that works from bulk materials.
It looks like a fun project!