Okay, here's the Mayo Recipe modified—you can't use all coconut oil or it WILL solidify:

Makes 1 generous cup

2 egg yolks
1/2 teaspoon salt
1/2 teaspoon Dijon mustard (optional)
1 tablespoon fresh lemon juice
2 teaspoons unseasoned rice or white wine vinegar
1/2 cup liquid refined coconut oil (neutral tasting)
1/2 cup macadamia nut oil (or olive oil or hi-oleic expeller pressed sunflower oil)

Put the egg yolks, salt, mustard, lemon juice, and vinegar in the food processor. Pulse 4 or 5 times to combine well. Remove the feed tube, if it is still in place. Run the machine and pour the oil through the feed tube in a thin (less than ¼ inch wide), steady stream until completely incorporated. The mixture will thicken as the oil gets worked in, and the sputtering will diminish by the time the sauce becomes super thick and creamy. It should take 2 to 3 minutes to add the oil.

If the mayonnaise seems overly stiff, work in water by the teaspoon. Taste and adjust the flavor for extra salt and mustard, pulsing the machine to blend the ingredients. Transfer to an airtight container, cover, and refrigerate for up to a 2 weeks. To maintain freshness beyond 2 weeks, add 1 Tbs. whey (drained from yogurt)

You can also check out this video and recipe—but it's still easier to do it in the food processor (and get it out of the work bowl):
Coconut Mayonnaise