The machine may have grease nipples, but in some cases, putting grease through them can be BAD news. The grease will solidify, so that the oilway is blocked and the bearing gets no lubrication.
It may well be that the correct lubricant for that particular point should be oil.
If you need an oil gun, I can recommend a Rielang, may seem costly, but does not leak and works at almost any angle.
HTH
Howard