Is there anyway to have a father give up his financialobligations to a child without giving you all of their rights?

Not that I know of. You have to pay unless the child is legally adopted by someone else. Sorry. You made the kid now you pay.

If the custodial parent has a new partner to adopt, new obligations can be stopped, past due obligations may often still be collected

You can't "give up" your financial responsibilities, but still have all rights to your child... haven't you ever heard the saying "you can't have your cake and eat it to?".

You will be required to pay child support unless the time comes that the mother has a spouse that wants to adopt the child and assume all responsibilities (financial included) but in that case you will need to relinquish ALL your rights.