I've done a quick search and you can shop online at the Iceland website. You can find the link to the appropriate store on my webpage here. Unfortunately, they don't do home deliveries, but are thinking of starting this service eventually.
Iceland's Los Cristianos branch is found at the base of the Costamar tower, near the Arona Gran Hotel.
Hiperdino's website says they do free home deliveries for shopping that totals more than 60 euros. There doesn't seem to be any scope for online shopping, though.
There's a smallish branch of this supermarket in Los Cristianos, just near the Costamar, on the other side of the road.