This sentence means, word for word: ... make birds' happiness, or ... happiness of the birds.
That is working like possessive case: le bonheur des oiseaux, where "des" means de-les (contraction) for of-the
Thank you for pointing that out. But couldn't it also be his, technically? Apparently the desired meaning is that is is a tree which has fruits but could the French not also mean that it is a person that gives fruits to the birds?