Do I need an attorney to get a child custody agreement modified?

You need to file for modification and agree to a joint stipulation that must be approved by the court.  When you do that, it will have an impact of child support obligations.  Thus other documents may need to filed. 

There are less expensive ways, but these may be less wise in the long run.

What you want to do is modify the custody order.  Although you can agree to the modification the court will need to sign off on it.  Courts take great pains to make sure that the best interests of the child(ren) are met in custody matters.

Additionally, most states have child support guidelines that must be adhered to.  It is a worksheet that takes in to account the income of both the parties as well as who is the custodial parent.  I doubt that you would pay nothing for the child who resides with your ex spouse even though you each have one child because you are working and your ex is not.  It would be best for all parties for you to seek legal help with all this.  This way you can get it right from the start and not waste time and money seeking to modify the order only to have the court shoot it down.