My daughter is going to be three years old soon and her biological father has not been a constant in her life providing her with nothing emotionally or financially.My current partner is the only father she knows and has supported her.How can we get the biological father to sign over his rights?

You ask him very nicely. If he refuses there is little you can do.

You can't make him sign over his rights if he doesn't want to, but the court can order him to pay child support and garnishee his wages if he doesn't do it willingly. If he doesn't really care about his daughter, confronting the possibility of paying child support may make him easier to persuade about giving up his parental rights. It worked with my stepdaughter's birth father.

Petition the court for your partner to adopt her. You'll have to show that you've made every good faith effort to contact the biological father. Once you do you can request but not compel him to sign over his rights. If you're unsuccessful in locating him despite making every reasonable effort (and be prepared to document this for the court), then the adoption can proceed without his consent.