SC4 lathe grease points - how to lubricate non-zerks

Hi all.

Trying to lubricate the grease points on our two SC4 lathes, but the grease points are not zerks, just little holes blocked by spring-loaded ball bearings, I presume. So there are no zerks to which a grease gun can be attached.

How do you grease these points? Do you have to use a push grease gun with a conical nozzle? Using a push gun with a flat nozzle tends to make grease squirt out sideways.

What say you?