If you are OK with Wiktionary as a source then compersion does have the meaning you are looking for.
1. The feeling of joy one has experiencing another's joy, such as in witnessing a toddler's joy and feeling joy in response.
2. The feeling of joy associated with seeing a loved one love another; contrasted with jealousy.
There are a number of definitions in Wikipedia within the topic of Polyamory and therefore are predisposed to be defined in terms of sexual joy. http://en.wikipedia.org/wiki/Polyamory#Compersion
The discussion regarding that page at http://en.wikipedia.org/wiki/Talk%3ACompersion#Etymology.3F puts forward an etymology of the word offering
... he says it was created by the group via Ouija board (a device of which Kerista made extensive use for decision making), prompted when a couple of the female members were discussing positive feelings they had about their male partners with others and thought "there ought to be a word". It was not consciously invented from any roots.
see http://en.wikipedia.org/wiki/Kerista for the Keristans (who also claim polyfidelity and polyintimacy as words of their own coining - but note that these are based on Greek and Latin roots not a Ouija board)
As noted in a comment, there's no mention of it in the OED but there is (the very obsolete - 1500's) conperseyner and compercioner which are variants of comparcioner which has the definition of
One who shares a possession or inheritance with another; a copartner.
I'm not saying that is the origin of compersion but it's not too hard to extend that to simply sharing with another to cover the emotion of joy without the need for the joy to come from sexual activities.
Wiktionary contributors, "compersion," Wiktionary, The Free Dictionary, http://en.wiktionary.org/w/index.php?title=compersion&oldid=31307300 (accessed January 16, 2015).