On the subject of "no puncture" tyres, there was a brand called "Care Free" that was sold some years ago that was a solid (slightly compressible to allow a bit of "give") band around the rim. Unfortunately from what I heard they had poor grip in the rain.
Having said that, I've just done a quick google and found the following site
http://www.kairfree.co.uk/ which seem to be the same people with a slightly different product.