How to change country on app store without credit card

From Why can’t I select None when I edit my Apple ID payment information? - Apple Support :

When you change the country or region of an existing Apple ID, you must provide a payment method and update your billing options. If you want to remove your payment method after you change the country or region, you can change your payment information to None.

You should be able to remove your card details after entering them.

If you don't have a card, and you are in the country that you trying to change to (you have to be in a country to use its store), then you could try contacting iTunes Support and see if they can help : http://www.apple.com/support/itunes/contact/