I assume there is some sort of plunger or piston that needs to move freely inside the cylinder, and would suggest either a precision spray valve or a radial spinner valve.

The spray valve uses a low volume low pressure (LVLP) design to apply an even coating of material, while the radial spinner dispenses fluid onto a rapidly spinning disk to produce a uniform band. I have seen both produce excellent results -it just depends on whether you want to apply lubricant over a larger area or put it in a specific location.

Depending on your production volume and budget, the valve could be stand-mounted and controlled by the operator or incorporated into an automated dispensing station.