Sproing is certainly used often enough. A search on Google Books returns plenty of examples. I always like it if a word can be found in at least one standard dictionary. In this case, the only entry I could find was in the rather specialist reference work,
Ka-BOOM! A Dictionary of Comicbook Words on Historical Principles:
SPROING [The Twisted Tantrum of the Purple Snit #1, 1980] The sound made when the spring of a spring loaded mechanism is released: also SPROOOING [The Ren and Stimpy Show vol.1 #6, 1993] A springing sound
Despite the lack of dictionary support, I think
sproing should be allowed.
Interestingly, I feel it's not a case of pure onomatopoeia. The
-oing part is certainly onomatopoeic, but the
spr- beginning doesn't seem to me to be part of what a
sproing! sounds like. I think it's there to remind us of the word
spring. It would be interesting to know how other languages represent this sound, but alas, I never thought to acquire a multi-lingual comic book collection.