The `American Idol` judge gave three-year-old Max and Emme - her twins with estranged husband Marc Anthony - the nickname when they were babies because she felt they resembled the hairy fruit.
She explained: "The twins are so good, they`re about to turn four. They`re my coconuts, that comes from when they were little and in their cribs and started growing hair, it looked just like a coconut to me, they both look like coconuts.
"I have this beautiful necklace which was given to me at Christmas, there are two coconuts and their initials on it."
Jennifer - who is now dating dancer Casper Smart - also revealed her former boyfriend P. Diddy gave her the best advice she has ever received when she was beginning her career, even if he didn`t express his message very kindly.
She told TV talk show host Jay Leno: "I had a lot of mentors, Puffy aka Diddy now, when I first met him I was making my first album and he gave me a lot of insight into the music business, he helped me a lot.
"He did say one thing to me that was funny, I was recording music for my first album and I played a song for him and said, `What do you think` and he said, `I hate it. It`s not good, it won`t be a hit,` and I said, `I love it`, standing up for myself,` and he said, `Good, you can listen to it in your living room because you`re the only one.`
"It stayed with me because he`s right - as an artist it`s not just about touching you, everybody has to relate to it, that`s the main thing so i really learned from that, even though he was tough with the message.