Yes, you can file 1 state return now and the other later. You do not have to file the 2 state returns at the same time.
Is one state a resident state return or part-year resident return, and one a non-resident state return? If so, you should prepare the non-resident state return first before any resident or part-year resident returns, so that everything will populate and calculate correctly on the resident state return and give you credit for any state taxes paid in the other state. See the 2 FAQs I left you in another posting below.
Did you efile the Federal return? If you efiled the Federal return, it has to have an efile status of "accepted" before it will let you efile any state return. If you printed and mailed the Federal return, then you cannot efile the state returns.
Here is some additional info to go with my post above. Here are a couple of FAQs that might help, depending on your specific situation:
Non-resident state return
Part-year resident state return