Others here have had success with macadamia oil. I've tried with avocado oil + extra-virgin olive oil and it works, but it does get kinda solid in the fridge. I've also tried bacon grease and it gets solid too. Here's a post about doing it with ghee. I can imagine that would get REALLY solid:
Homemade Ghee Mayo | Mark's Daily Apple
And here's an awesome Food Lab post about the science of mayo and some animal fat mayo recipes, though it does call for using canola/vegetable oil:
The Food Lab: Animal Fat Mayonnaise | Serious Eats
Just found this page:
So it looks like macadamia is slightly lower in saturated fat than avocado, but avocado is higher in PUFA, so if I had to guess I'd think avocado would be better for mayo from a texture/emulsion standpoint.