For father, we have daddy, dada, papa, poppy, etc. For mother, we have momma, mommy, mama, etc. Is there a term of endearment that fits either role? I've racked my brain thinking of one and I can't. For children, the only gender neutral one I can think of is 'kiddo', or 'kid' to some people.
As you note in your question, there's not a lot.
After I posted this answer I saw some people had responded with comments concurrently. I didn't think of "folks" but that's probably the best one. Ermanen deserves credit for that one though.
Here's what I thought of:
SNL popularized the term "parental units" and the term entered the popular culture and some people probably use that term sometimes in an ironic, affectionate way (ironic because the term was meant to be the least affectionate way of referring to a parent in the SNL scripts). I have witnessed the term used in popular movies, Internet chats, etc. It's even in the dictionary.
People with a Buddhist background may say something like "honourable ancestor" as a very formal and respectful way to address either parent. Similarly, a very old term that people in the past could use sometimes was "progenitor". Both "ancestor" and "progenitor" refer to any ancestor, not just the direct parents, but they can (perhaps more accurately could in the past) be used in a very respectful and even affectionate way to refer to parents.
In know one person who calls his parents "old people", or sometimes "old person" individually, which may not be a term of endearment in every household but he gets away with it.
For children besides kids/kiddos/kiddies which you mention, there's also squirts, rugrats, bambinos, cubs, juveniles, sprouts, whelps, youngsters/young people/young adults, and youths to name a few.
This post helps a lot: http://genderqueeries.tumblr.com/titles
It includes a bunch of gender queer titles for all types of relations. They provide the following for parents:
- Parent; neutral, formal.
- Per; neutral, short for parent.
- Par; neutral, short for parent.
- Dommy; queer, mixture of mommy and daddy (note: sounds like Dom/me, a BDSM term)
- Maddy; queer, mixture of mummy/mommy and daddy.
- Muddy; queer, mixture of mummy and daddy.
- Moddy; queer, mixture of mommy and daddy.
- Zaza; queer, based on mama and papa/dada.
- Zither; queer, based on mother and father. (Note, zither is also the name of a musical instrument.)
- Baba; neutral, based on mama and dada. (Note, baba means dad in some languages and grandmother in others.)
- Nini; queer, based on the N in NB, similar to mama and papa/dada.
- Bibi; queer, based on the B in NB, similar to mama and papa/dada.
- Cennend; neutral, Old English (Anglo-Saxon) meaning parent.
- Cenn; neutral, short for cennend.