If your child will grow up among the American melting pot culture in addition to her dad's family culture, then I think it's important to consider how "normal" in Filippino culture might be received/reacted to in her wider community, since your daughter will be dealing with those reactions. Personally, I would not want to grow up in an English-speaking culture with a known nickname of Din-din or Nadz.
If the nickname must be repetitive or near-repetitive, then your NiNing seems best from your list, but I also think the suggestion of DeeDee/Dede is great and seems to fit comfortably all 'round.
In general, I don't think nicknames are really necessary (obviously in your case they are); often they do come about naturally and have nothing to do with the person's name. Ultimately, your daughter will decide what she likes to be called, even if it's something you don't care for. Personally, I have found that people who like you nickname you. I can call someone up on the phone who's known me a long time and say "hi, it's *my name*" and they will come back with "oh hi, *common nickname* ", despite my never ever having introduced myself by or signed my name by that nickname. I have a couple of parent-given nicknames and also one given by a family friend that stuck and is used occasionally. The nickname I use for myself, among my close circle, is one of the parent-given ones. Generally, I go by my full name and announce/introduce myself that way.
This message was edited 11/10/2015, 12:24 PM