From the outside, it would appear that it's a simple 'bellows' type, which is a variation on the 'squeeze' type. Think of it like an accordion. When you push down, the bellows collapse and force whatever is in them out through the one-way valve in the spout. When they spring back up, a vacuum is created which allows ambient air pressure to force liquid from the reservoir through the other one-way valve into the bellows chamber.
There are 3 ways that immediately come to mind for calibrating the amount pumped per stroke. One is to just make the bellows chamber the proper size to contain that volume. The second would be to use an off-the-shelf unit that's overly large and fill up the excess space with something like insulation foam. Third would be also with an oversized unit, but with some sort of mechanical stop to prevent full travel of the stroke.