As far as I know, the 3 items on the small table area, and the 1 furniture item next to Grams is all you get each day. Thanks for telling me the Club Tortimer form won't vanish for you after you bought it; this means I won't have to buy it until I can go online.
Some items seem to be more common than others, and show up more frequently. you just have to suffer through it. :/ --- Currently playing: Animal Crossing: New Leaf
On the bright side, if you use Club Tortimer the items seem to change whenever you leave and go back. I honestly don't know how it works - if there are a set number of Club Tortimer islands set up, and each of those has set things it's offering, or if a new random island is generated when someone enters it. But at any rate, you can go to some Club Tortimer islands if you're hunting for something specific.
(Don't know exactly how many items are offered, sorry, and I'm too lazy to try to check right now. :p I know of at least about 5 or 6 clothing items, a mermaid set and cabana set which I'm assuming are around 11 pieces each, the hibiscus starters, and multiple dive suits, off the top of my head.) --- Please insert witty quote here.