Sounds as though you have the old “ straight” nipples as used on lots of older kit – vintage cars, Suffolk and Ransomes mowers to name several. You can possibly pick up a pump type gun with a suitable connector at an auto jumble . If lubrication is more important than originality just switch the nipples to modern “snap-on “ ones. ( Type, not the tool seller!). Threads could be BSP or UNF – a Monro tiller collector can probably advise you.
A trick that was used by old school mechanics was to lay a piece of thin clean cotton cloth over the nipple and apply the gun connector over it providing a seal while still allowing grease to be forced through it.