As I go through the New Jersey (NJ) nonresident return and then complete a New York (NY) resident return I was able to complete both returns without errors on either state return. See the images below.
Your nonresident return must be completed first, then the resident return so that it picks up the credit when you select 'Credit for Taxes Paid', then 'Taxes Paid to Another State'.
If you have done the returns in the correct order, review your entries and be sure to go through each screen until you are finished with all and returned to the summary of your state taxes. If you have not done them in the correct order, you should delete them to start over.
BEFORE you start over and even if you don't need to start over you should clear your cache and cookies. It handles many issues that seem nonsensical on a regular basis.
Watch to be sure you are selecting 'all time' as example. Do not use selections like 'last hour' for those browsers that give you options.