here is a pretty authentic looking and working sling that you can make for maybe $5 or less.
how:
go to the hardware store, walmart, or garden store and buy a roll of 1 mm jute or sisal or hemp twine.
take this, and braid it into the sling seen here:
http://slinging.org/20.htmlto this, you can add a pouch cut out of a leather chammy (also from walmart) used to polish cars and stitch it on the sling in this fashion:
http://slinging.org/articleimages/22/apacheSlings.jpgthough only using the braided part workes fine, even great. that is the sling that i used for a long time, and it works well. when you add the leather pouch it is called an apache style sling. the only difference between the two slings is the pouch sewn on to the braid.
looking at alot of different "artist's renderings" and classical referances, just a split pouch seems prevelent, though it is often depicted as having leather sewn over the braid to protect the cordage material, as seen here:
http://slinging.org/galleryimages/022_19ass.jpgand here:
http://slinging.org/galleryimages/BalearSlingContest/detalle.jpgit is a little hard to see, but they are pretty good examples.