My daughters biological father does not want any rights to her and is OK with my current boyfriend to adopt her, but I'm not sure she can be adopted as we are not married or living together? What other opptions do we have? I don't want her biological father to pay child support or have any rights to her!!

First, this is a legal question not an Adoption question and has been moved to this forum. Please be more careful in the future with choosing an appropriate forum to post in.

You need to consult a Family Attorney in your area. Most areas do require that a couple be married before a step parent adoption will be granted. You will, generally need an attorney to draw up the adoption paperwork which will include a relinquishment of rights from the bio father. So consulting with an attorney should be your first step to learn what requirements there are.

Without an adoption the bio father will continue to have a father's rights.

Until the child is adopted by another parent, the biological father will maintain parental rights and be subject to pay child support.
I most, if not all, states, you have to be married at least a year before your spouse would be allowed to adopt the child and the biological father could relinquish his rights.
Now, even though the biological father has parental rights, it doesn't mean he has to exercise them.
Do you already have child support established in the court system?
If not, you could just come to an agreement that he doesn't want any involvement with the child and you don't want any child support.
But even doing that, at any time, either of you could file for child support or visitation.