Unrefined coconut oil is only safe to 350 degrees, but refined coconut oil is safe to 450 degrees. It doesn't taste like coconuts, either, but I don't know if you can use it for mayo because it's solid at room temperature. In general, refined oils will have much higher smoke points than unrefined oils.
Ghee is safe to 480 degrees, tallow to 420 degrees...
...in theory. Remember that all smoke points are very approximate, and depend on the source food and degree of refining. You've got to try these things yourself, in your own kitchen, and see how they taste to you.