I am divorced and paying child support in the state of Massachusetts. The mother lives in New York state and has done so for ~2years. I am planning on moving to North Carolina later this year for a different job and the mother, unemployed during those two years, is now accepting a job in New York.

What do I need to do to modify the child support based on each of our new incomes and with which court can I do this? Mass, NY, or NC?

It is typically whatever state the divorce decree originated in

I would first contact the DSS offices in Massachusetts where the Order is in place, and ask them. It is possible to continue paying under Massachusetts law even if neither parent lives in that state. However, you and your ex-spouse can also choose to pay under New York. If it is New York, they have guidelines based on the percentage of your net income. The State of New York presumes the custodial parent will be providing at least a portion of the support, so the amount paid by the non-custodial parent isn't based on how much the custodial parent makes. In New York, barring unusual circumstances, it is 17% of your net income for one child, 25% for two, 29% for three, 31% for four, and 35% for five children. New York would modify the order to coincide with the State's guidelines. Her income would not be relevant. How much you pay in taxes, however, would be very relevant.

North Carolina also has guidelines, but they are not based on percentages. And, I think North Carolina law is least likely to apply because the custodial parent has no tie to the state. The amount you pay in that state based on monthly gross combined income of the non-custodial parent's household (!! ). Here are the guidelines in a nut shell.

North Carolina Divorce Law - the NC divorce law site

Look for your income and look at the number beside it that matches the number of children you have. Note that the lower income earners get hammered, but the top earners barely pay squat. For example, a person making 25,000 a month would only be required to pay $1819 in support, less than 10%, whereas a man who makes $4000 a month has to pay $715, almost 18%, and that's of GROSS income. Unless you make a killing, if you would like to starve or would prefer to live in your car, then I recommend going with North Carolina law. (Stay away from North Carolina law)

If New York law is not favorable to you, I would recommend sticking with Massachusetts law, and making your case in that state.