If my cousin and the father of her baby want to sign their rights over to me as the baby's permanent placement, do my husband and I need a lawyer or can we just do the paperwork?

It is best to use an attorney ( they should not be that expensive) my cousin is doing something similar and thiers will cost about 750 since everyone is in agreement and it is just paper work to be filed with the court. Since you want it all correct in case someone changes their mind in a year or two.