A usually adequate answer to feeding the spring loaded ball oilers is to use a normal pump action oil can with a piece of clean cloth over the oiler to make a seal between the oil can nozzle and the ball surround. Best to have a can with a flexible spout so you can hold the can part more or less level in one hand whilst using the other to get the nozzle square on the oiler. May take a little experimentation to find the right piece of cloth, lint free of course. I think I settled on a double thickness of old bed sheet.
Not a fan of ball oilers . I find them difficult to clean as well as being a pain to fill so tend to replace with something else wherever possible. Whenever I’ve gone under a ball oiler as part of a strip’n clean operation there has been significant amounts of debris beneath.
John H asks about oils for lathes and mills. I use Castrol Hyspin AWS 32 and Magna BD 68 mail ordered in 5 litre bottle from RS Components pretty much indiscriminately. The Hyspin will serve for the light oil requirements of most machines and the Magna is fine for bed slide-way and heavy oil requirements. Magna makes a great oil can oil for round the house jobs too. In home shop use clean and plentiful oil is far more important than exact makers specification. Frankly the detail properties of oils to the same name or nominal specifications have changed greatly in the years since most of our machines were made. Usually to our benefit.
Clive