Have I used "Such a" in an appropriate way?
Congratulations for having such a little bundle of joy.
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"Such a..." emphasizes whatever word you follow it with. As @peter mentioned, the word your emphasizing here is that the bundle of joy is little, which would be uncommon.
Used before a noun or noun phrase to add emphasis. CED
Such a should be used in the same way, but for singular countable nouns.
Long story short, what you have said is grammatically correct, but probably not exactly what you're aiming for.