My pronouns are Sh'e and H'er. The placement of the apostrophe is very important.
I am the only one I am aware of that uses these pronouns.
They and them is ok with me as well, as is she and her.
But my preferred is sh'e and h'er. Because its the only visual you can get that is accurate for who I am.
I made them up. I assume that makes it constructed.