Any decent digital one should be able to do that I imagine. I've got an entry-level Siglent[1], it can do 1 microHz and up. Or am I missing something?

[1]: https://www.siglenteu.com/waveform-generators/sdg1000x-serie...

The tinySA can also be used for that, it's not only a spectrum analyzer, it can also generate signals and optionally modulate those for you.

edit: https://tinysa.org/wiki/pmwiki.php?n=Main.Specification here says it works from 100kHz for the low output. When I just tried it did let me select 60kHz and turn it into output mode. Haven't hooked it up to a scope to see what it does. Sorry no time to set it all up now. 60kHz is very low though, if you browse AliExpress then I'm sure plenty of signal generators will offer that for a really low price (cheaper than the tinySA)

edit 2: Sorry my European brain kicked in and missed you are looking for a 60Hz one that is very precise and not a 60kHz one. I'd better get some sleep.

Check out the function generators from FeelTech on Amazon or AliExpress, like the FY6900 or FY6800. They’re cheap in a flimsy plastic case, but they’re good enough for many applications.

Im not sure how well it would work, but for a low cost solution try your PC's sound card. Reasonably low distorsion and sufficient frequency accuracy.