I forgot Hawaii Surfboard Rentals do SUP. Service is great boards are in good nick and they deliver to your door.
I think most of the posts mean Koa Board Sports on Koa Ave behind the Hyatt, not Kona. I wasn't really paying attention either, but I didn't notice ay SUPs at Koa Board Sports.
Moku on Koa Ave is the one with the Mexican restaurant upstairs. I didn't check this one. It was reviewed here:
www.seabreeze.com.au/forums/Stand-Up-Paddle/SUP/Hawaii-visit-board-hire/There is a guy who hires SUPs in the same complex as Koa Board Sports - Big Wave Dave www.bigwavedavesurfco.com. One of his SUPs looked like a pretty reasonable surf SUP.
I couldn't find a convenient enough SUP rental in Waikiki and didn't have a car that week so didn't bother grabbing one from Ala Moana. Mostly surfed and just paid rip off prices for OK-crummy condition NSP SUPs from Rentals on the beach when I felt like a SUP. I thought the NSPs were fun.
I do not know where the Blue Planet shop in Ala Moana is, but you could (if very, very keen) walk a SUP from the Surftech shop to the beach at Ala Moana and paddle it around to Waikiki. It is a couple of blocks to walk and a fair bit of a paddle (with a pile of surf breaks) - but was just too much effort for me.
For North Shore there is Surf and Sea at Haleiwa who have a great range of SUPs. It would be a good day trip if you are only staying in the Waikiki area. I was surfing here but it looked like a really good place to SUP in small and large surf and on the flats in the bay.