Oiling/Greasing smaller linear bearings

Ive got some MGN15 rails and bearings and also some 12mm versions.

I cannot find a little oil can with a small enough tip/nozzle that will press on the little ball and fill the bearings with lubrication.  What are you guy using for this purpose?

I also have varying sized syringes, but I dont find them to fit that well in the little "zerk".

The oil just comes out of the hole im putting it in.  Or are you just using the syringe to put lube on the rails/screws directly and not into the bearing blocks?

The pic shows the smallest of the nipples. (For my Zaxis 12mm rails)

The syringe that's there is 0.050" dia.  It's the closest size just smaller than the hole. But the ball of the nipple seals off the dispensing hole of the syringe. If i try and angle it, the oil comes out the top. I don't feel like anything is getting into the bearings. 

It's even worse for the bottom bearings that are inverted.

I see.

I'll try the smaller syringe and slide it between the wiper and rail for the small ones and see how that goes.

I'm just used to larger machines that either have auto lube systems or large enough nipples that your standard hardware store oil can brass nozzle fits perfectly. It's enough to depress the ball and has enough pressure to fill the blocks. I usually fill until it starts to come out of the wipers. 
This is particularly handy when the nipple is upside down and you have to force lubrication in the upward direction into the bearings.