So until there are better laws I'd like to enumerate what we can do today and ask that you contribute too. I'm one of those who unless the child was intended simply will not pay.

  1. Reduce your income to zero. If you own a company, transfer it to someone else or a board and acquire services from it by way of contract(you may loan an apartment, a car, food etc.). Child support is calculated from income.

  2. Before the child is born, move to a country without an extradition agreement. Acquire citizenship. Renounce prior citizenship. As you've changed jurisdiction you're no longer subject to law in the former one.

  3. Contest being the father in court, but deny paternity testing citing the fourth amendment. Finger pointing should not be enough for you to have to disprove anything. Child support demands should require evidence that you're the father.

These should all be legal too. Unfortunately, due to sexism, you're unlikely to succeed with 3. (see here) as men's bodily autonomy is not respected. For this reason I'm currently against the right to abortion and will side with religious fanatics on that one.