Commissioned by Capitol Records and made by George Barris in 1966. Supposedly 5 were built for the boys themselves and they were called 'Mini Surfers'.
These special Mokes came with candy stripes both in and outside, a special fringed canopy, golden record wheel discs, 8-track sound systems with removable speakers, chromed bumpers and fake air intakes on the bonnet.
The seats were made of red and white fur fabric, and the surfboard on top was a Dewey Weber
Supposedly another 20 were built to give away to radio stations throughout the US to be raffled in special Beach Boys competitions.
A May issue of Classic & Sports Car magazine had an article about Barris and mentioned these

http://www.smileysmile.net/uncanny/index.php/beach-boys-with-george-barris-kustom-buggies
https://s-media-cache-ak0.pinimg.com/originals/75/8d/e7/758de7b323314fd42d74be39c3465881.jpg
http://stiffspeed.co.uk/post/162723444754#notes
http://maximummini.blogspot.com/2014/04/the-beach-boys-and-their-mini-surfers.html
at least one is sitting in a garage gathering dust
https://www.facebook.com/groups/140112802865265/permalink/724249964451543/
in Nov 1966, on Monday the 7th
The Beach Boys: The Definitive Diary of America's Greatest Band, on Stage
and at the 4:18 minute mark