I have both the Marconi TF-2304 and the Heathkit IM-4180. Both work pretty well. The Marconi will automatically tune to the carrier frequency, while you have to manually tune the Heathkit.
As others have mentioned, you can also measure FM Deviation with a spectrum analyzer. I have a video on this (see below).
You can also measure deviation without any special equipment using the Bessel Null method - I have a video on this too (see below again).
Yup, watched those videos, but not thrilled with the results I got, for various reasons. I don't have a SpecAn. Tried to use the technique you show using an RTL-SDR dongle as a "poor man's SpecAn", and got wacky results - and have no idea if the problem is the dongle, the transmitter, or, most likely, PEBCAK.
I'm going to give the Bessel Null method a try next, using either the dongle or my handheld Yaeus radio (I don't currently own any other recievers that can handle 144MHz), but it's a little bit annoying since my transmitter isn't rigged to accept an arbitrary tone input, just the mark and space tones from APRS. (an obivous mistake that'll be fixed in the next revision of the PCB). So I need to bodge in a wire to let me connect my signal generator to the TX input.
That's one of my issues - when both the transmitter and test equipment are jerry rigged, it's hard to tell if an unexpected result is a problem with one or the other....
Which is why I want an actual meter that I can rely on, to rule out the test gear as the suspect.