If you put an Aura card onto the battlefield with Songbirds' Blessing's triggered ability, you choose what it will enchant as it enters the battlefield. An Aura put onto the battlefield this way doesn't target anything (so it could be attached to an opponent's permanent with hexproof, for example), but the Aura's enchant ability restricts what it can be attached to. If the Aura can't legally be attached to anything, you won't be able to put it onto the battlefield, and it will be put into your hand by the next part of the effect.