You can't. Not like that, anyway.
First, it is the child's right to his or her parents as much as the parent's right to his children which is at stake, and the law does not permit one parent to unilaterally revoke the parental rights of the other parent (or his or her own, for that matter).
Bearing that in mind, parental rights may be terminated (1) by the state, following a minimum of 18 months of CYS supervision, or (2) by the other parent IF there is a putative adoptive parent waiting in the wings. Under the latter scenario, the parent who stands to lose his parental rights has an opportunity to object to the adoption (and consequent termination).
But where there are two living parents, the law requires two living parents. Custody court and child support are your best bet.
If you and your boyfriend get married and the father continues to be absent and your new husband wants to adopt the child, you will be a position to file a Petition to terminate his parental rights. The court will not terminate his rights without a simultaneous adoption. You will need to meet with an attorney to prepare the paperwork.
My response is based solely on the limited information contained in the question. It is not meant to substitute your attorney's advice.
You don't have a "right" to have another parents custodial rights terminated due to being an absentee parent. A court in some circumstances may terminate rights, but as the other attorneys have noted, it would require an adoptive parent and it can be challenged by the biological parent. Your child's emotional confusion is a valid concern, perhaps you can preempt any later problems with counseling
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