I was seeking decent cardboard or fibreboard tubes myself this last few weeks. If you want anything larger than a postal tube or wine bottle tube then you will find it difficult finding something that comes in two sizes that will nest together, unless that is you have them made to order. This is possible and there are a few suppliers who will do it, although they charge a hefty set up fee to set the measurements up on their machines. Their website is:
www.essextubes.co.uk
Although carpet tubes look about the right size they are not really good enough as the wall of the tubes are very thick, meaning there is very little room for any load. Similarly piping from a plumbers merchant or builders merchant is plastic and therefore very difficult to get paint to apply so that it survives wear and tear.
However I did find something that will help you make decent perfectly round tubes/cylinders of your own to a large range of sizes very cost effectively, the steel rings that Lampshades are made out of only cost a few pounds and come in a range of sizes and you can get them from
www.fredaldous.co.uk in Manchester.
Hope this helps.