Absolutely, though whether you have easy access to the raw ingredients where you live is another matter—pigs' blood for a start. Apparently, most black puddings in the UK are made from dried blood not fresh blood and that usually imported:
Black Pudding from www.cumberland-sausage.netActually, VERY sad to say, virtually all the black pudding produced in the UK is made from reconstituted dried (powdered) blood imported - in the main from Holland. Our wonderful Food Standards Agency - who's [sc. whose] function in life is actually to restrict the activities of would-be mass poisoners, have failed to realistically interpret the (inevitably European) regulations concerning the collection of blood, and if they restrict supply to stuff coming from another 'member state' - immaterial of the quality - the don't have to [not sure what that means!]. But there we are; we probably aren't talking much more than 2,000 or so years of tradition after all....
But, yes, it can be made at home and recipes do vary and not all have cereal filler—and those that do don't necessarily use a gluten-containing grain.
Your local library may even have a copy of the book or be able to get it on inter-library loan.
Alternatively, you may be able to buy a barley-free black pudding direct from the maker:
Google: gluten free black pudding