Question Author
Thanks everybody for your answers, and my apologies for not responding. I used to get an automated e-mail from the Answer Bank every time somebody responded - but this doesn't seem to happen any more, so I just assumed that there were no responses.
There still doesn't seem to be any definitive answer to my question, and I suspect that there is no such word. A friend of mine suggested that there may be a possible answer in either finding the Latin for 'sibling' (the roots of 'fraternity' and 'sorority' are the Latin words 'frater' and 'soror'), but there seems to have been no such word in the Latin language.
There is also one language (at least) in which there is a plural noun which means 'brothers and sisters'. I thought it might be German, but all my memory dredges up from my 45-years-ago learning of German is 'gebreudern' and 'geschwestern' - 'brothers' and 'sisters'. There is, I feel certain, a language in which there is a single word for both, and from which we could perhaps invent a satisfactory English word.
Any more thoughts here?