My tool is called the "Rejuvenator." I just used it today to unclog two fittings on my loader.
There have been other posts on this subject, elsewhere. These unclogging tools seem to get a bad rap (pardon the pun), but I've used the Rejuvenator five or six times and it's done the job each time. One criticism is that dirt may be forced into the bearings. Well, maybe, but something tells me the risk of this, or the impact of it, is truly overblown.
It takes a little finessing but you get the hang of it. Sometimes you have to repeat the operation several times.
Be sure to bleed any air from the oil chamber. Just squirt a little oil out.
Another tip is to take pressure off the part the grease fitting serves. For example, don't try to unclog a fitting on a loader with the loader up in the air!
Finally, don't tap too hard. A steady, firm tap is what you want, to slowly force the oil in.
I don't mind "futzing." At least I don't have to futz around trying to research and buy the right-size zerk.