I believe you are correct.  If it is NJ generated income, you can still file a NJ return for your client if necessary whether or not there is a state K-1 indicating that it is NJ sourced income.

Have you been asked to prepare the 1041, or the beneficiary's 1040, or both?  A state trust return should be filed for both Maryland (if that is where the trustee or beneficiaries reside) and New Jersey (if there is income from that state).  Beneficiaries should receive the state version of Schedule K-1, for both states.  They may show the beneficiary as either a resident or nonresident.  

I am preparing the 1041. There is no income in Maryland. The k-1 is for a Virginia resident and the other is for a Maryland resident. Why should they receive a Maryland k-1 ? They should not be taxed in 2 states for the same income? There is no interest from the checking account in Maryland. The property is generating net income in NJ. What would be on the Maryland k-1? 

If it's a MD Trust a MD trust return should be filed. 

If the income is taxed in 2 states (likely) one state will give a credit for tax paid to the other state.

Why? Because.

The Maryland K-1 for the Maryland resident shows all of the income from the whole world, because it's a Maryland trust for a Maryland resident.  The Maryland K-1 for the Virginia resident shows zero Maryland income, because there is no Maryland-source income. 

The New Jersey K-1 for the Maryland resident also shows all of the income, because it all came from New Jersey.  So that beneficiary will file two returns and figure out which state gives a credit for tax paid to the other.  

The New Jersey K-1 for the Virginia resident also shows all of the income, because it all came from New Jersey. Again, two returns with credit on one for tax paid to the other. 

If they don't like that, they should sell the place anyway before the next hurricane.