The This to That website suggests Weldbond and a few other types of glue.

You can use Elmer's glue (the white stuff) or Carpenter's glue (the tan stuff is a little stronger). Neither of those dissolve styrofoam, but try it first on yours. You can use toothpicks to strengthen the joint, too. Just jab some in halfway on one board, apply the glue and press the other board onto the toothpicks still sticking out. Or if you really want to get fancy, 3M makes a spray adhesive for foam board insulation, but it is expensive. I think it's Spray 78.

The Elmer's does take a long time to dry on styrofoam, so be prepared for that.

I have done several projects with Styrofoam. Try these styrogoo!

Styrogoo

Loctite PL300 Foamboard glue

Foam fusion

The wrong kind will melt the Styrofoam and can cause bad fumes.

I glue styrofoam together to use for my upholstery projects. I use 3M spray glue, Walmart sells it.

http://www.uline.com/Product/Detail/S-18767/Aerosols/3M-Super-77-Environmentally-Friendly-Spray-Adhesive?pricode=WY490&gadtype=pla&id=S-18767&gclid=CKOM9JeuusYCFQEdaQodolEG9A&gclsrc=aw.ds

The seat cushion & back cushion is comprised of about 6 pieces each.

Cool. I didn't think about using toothpicks. Looks like I have lots of options for gluing it together.
Thanks everyone.

Pooh Bear

Wouldn't it be better to just make one out of vinyl material, like companies do for bbq's or other out door equipment? I'm wondering if a round vinyl table cloth would work? Cut it to size, hem it and add elastic?

I'm wanting to use styrofoam for the insulation value; to hold heat in at night.

You know that solar blankets for pools are made of bubble wrap but in a heavier form. Using a layer of that floating on the top of the water would do a lot to help maintain the temp. We used the solar blankets on our pools with great success. You might check at some pool stores for remnants or old pieces. You would not need a very big piece for that. You can also try using the bubble wrap with the giant bubbles you can buy for packing but it won't last nearly as long.
The top on our hot tub, which is long gone now, was a hard shell but inside was filled with the little styrofoam balls like in bean bag chairs. Just a thought... sew up a big old bean bag cover! When that hard shell cracked those little balls were everywhere.

solar blanket at home depot for under $30

walmart solar blanket

at walmart

There for about a week when the temps were in the upper 90's and the lows were in the mid 70's the water was warm like bath water. This week has been so rainy the water is too cold to get in. I'd like to use my little pool for longer in the season.

I have been looking at a solar blanket. (Thanks for the links)
http://www.toysplash.com/poolaccessories/spasolarcover.html

I'm trying to find a use for all these styrofoam blocks. A cover seemed like a good idea. But the cost to make it about equals the cost of buying a cover.

Pooh Bear.

Spray on contact cement. I do it all the time at work. Auto supply or hardware stores.