I was married in the Catholic Church but I am divorced now. I did not get a annulment. The priest said I could not be a godmother, but I have my doubts.
Am I able to be a godmother at the baptism of my niece that I have custody of?
Being divorced may or may not be an impediment to being a godparent. It will in fact depend on several issues. Some divorcee are not at all guilty of any wrong doing within the marriage as may happen in the case of spousal abuse. Each case must be look at in its own merits.
If one is divorced and remarried without getting an annulment than one can not become a godparent.
So, what are the requirements of a Godparent/sponsor in the Catholic Church?
For Baptism, every child must have at least one Godparent and no more than two Godparents. If there are two Godparents, one must be a male and one must be a female.
A Godparent/sponsor must be a Sacramentally Confirmed Catholic who has already received Holy Communion.
A Godparent/sponsor should be at least 16 years old.
A Godparent/sponsor may not be the mother or father of the child to be baptized.
A Godparent/sponsor must lead a life of faith in keeping with the role and responsibilities to be undertaken.
A statement attesting to the good standing of the person proposed to be the Godparent/sponsor must be obtained from their proper parish. Or, if they are already members of a Parish, the pastor must confirm their good standing and ability to fulfill the above requirements. This statement should be presented to the Parish at least two weeks before the scheduled baptism. A person without this statement often called a Sponsor Certificate) cannot serve as a Godparent. Try to prevent embarrassing a person by asking them to serve as a Godparent/sponsor, knowing that they are not practicing the Catholic faith, are in an invalid marriage, etc., and will be unlikely to obtain this statement from their proper pastor. - Godparent/Sponsor
In short your situation must be made known to the pastor performing the baptism(s).
Can. 874 CIC says: To be a Godparent, someone must
3/ be a Catholic who has been confirmed and has already received the most holy sacrament of the Eucharist and who leads a life of faith in keeping with the function to be taken on;
4/ not be bound by any canonical penalty legitimately imposed or declared;
If you are only divorced (and living as single now), 874.3 could already be a problem.
I'm not 100% sure, but as far as I know canon law intends some kind of punishment in the case that a divorced person marries again or even only lives together with a boyfriend (or girlfriend).
So if you live together with another man, 874.4 will be another problem.