When I inquired, the client replied that a сиринет was a phonograph traditionally used to provide music in a pub-style restaurant.
That solved the immediate problem of how to translate the term: in the very non-technical context the word "phonograph" would do nicely. But I am interested in music history, and a music term that comes up with no relevant hits in Google is enough of a mystery to keep me awake at night.
Sleep works wonders.
The next day it dawned on me that the сирин- part of the word could be a phonetic spelling in Cyrillic of a word that used different vowels in its original language. I might be looking at a word that had a connection to sirens, either the Greek ones or the emergency ones.
Bullseye! The Pulsometer Sirenette was a ship's fog horn. Here are some pictures of Sirenettes (third row down) - they look a little like the amplification horn on a phonograph, don't they?[03.2010 NOTE: the picture gallery is moving hosts - I will revise the link once it is up again]
If anyone knows how pub phonographs came to be called Sirenettes in Russian (and whether or not the name was ever in widespread use) I'd love to hear about it.