Full-fat greek yogurt.
Hard cheeses (or soft ones, if you tolerate dairy well enough).
Don't forget that a lot of non-fatty things can be cooked in fat. I cook my greens (chard or spinach) in bacon grease and/or butter, with garlic and other seasonings.
For the purposes of your allergies, does coconut count as a nut? There really aren't that many others that I would use either. I don't even eat nuts all that often or all that much at a time. Most of my cooking is done with olive oil, butter, or bacon grease (in reverse order, actually). Nuts are handy for snacks for some people but not really necessary.
Also, I read a few articles lately that you might be interested in, if you can get your doctor to go along with it:
Overcoming Peanut Allergy