One that I have heard and want to pass along is "sigfig" Kinda borrowed from math as "significant figure". But it is a cute short term to refer to someone who is close to you without assuming gender.
I have been starting to use gender neutral terms for referring to partners because I have one too many times made a heteronormative statement to a new acquaintance who turned out to be homosexual. so, instead of asking "Who is your boyfriend?" I asked "Who is your sigfig?". And honestly, I have not had THAT many odd looks about it.
Also, there is this awesome blog
Here that has a whole slew of gender neutral titles for ANY relationship. Some of them are formal, and others are casual and cute.