I'm more of a "find your own, cheaper solution" type of a guy. for more permanent lubrication, use medium or heavy oil. you all have something to lube your chain, usually this is medium viscosity. if it does not turn into gel-like substance, go with that. otherwise, I always use heavy oil, usually 75-90 car gearbox oil. cheaper and much bigger quantities.

because there no close tolerances, you could go with light machining oil, but it's not hydrophobic and it will eventually be contaminated by water. I also noticed that light oil penetrates too quickly and most of the time you'll have greasy hands while driving.

edit: if you really want to use grease but don't know how to put into tight spaces, stick it into a syringe, mix it with a couple of drops of acetone, squeeze and let it evaporate. don't use paint thinner, as they'll eat your plastics and they evaporate much longer.