Put a flat plate across the gap. Add dead weight to the plate. Inject the liquid into the gap under pressure below the plate. Remove the plate. Clean up.
Injection pressure should be no more than 1/2 the contact pressure of the dead weight. Might require a little trial and error.
Spoon,
Depending how big this assembly is and how many you need to treat you might combine Ron's idea of sandwiching the parts with Berkshire's by adding the zerk to one of the plates. There is a bearing packer that uses this method to squeeze grease into bearings.
Is the gap between flat surfaces? Put a measured quantity of liquid on one surface, then assemble the parts. The liquid will spread throughout the assembled clearance. Calculate the volume of the clearance to determine the quantity of liquid to apply.
Is the gap between two cylinders? Cap both cylinders. Put a measured quantity of liquid in the bottom of the outer cylinder and push the inner cylinder into place. Force the liquid into the gap between them.