Coconut oil.
http://www.freecoconutrecipes.com/in...nut-mayonnaise
The recipe has some olive oil in it, but perhaps it's flavor may be masked by the coconut or you could omit the olive oil and go 100% coconut oil. Posters in this forum
http://www.lowcarbfriends.com/bbs/re...pes-ideas.html have done that and said it worked well.
I don't yet have any experience making mayo, but it's on my to-do list.