Since the only thing you need is a label for that exactly record for an app, which merely play it along with other random sounds, rather than attempting to recall some Russian onomatopoeia associated with spring (which, afaik, does not exist), I’ve listened your record fifty times in a row trying to abstract away from what I knew about it from you.
And I will tell you that the sound per se is no more a sound of spring than a vibration of a string or elastic band or anything else. Actually, it is most looks like варган – the primitive folk instrument which is common all over Eurasia: from Kirghiz steppes to the Far North.
So, forget about the spring. Simple дынь or дон, which are pure sound imitation and have no any particular sense, describes that very sound quite properly. No meaning – no any possibility for misunderstanding.
And finally: there is nothing wrong to invent your own onomatopoeia. As far as I understand, you said that the /bɔɪŋ/ is good approximation of that sound. Perfect, let it be боннь.