Death records are usually obtained from the County Clerk's office.
FamilySearch online has some Morris County Probate records that you can find at the following link: https://familysearch.org/search/image/index#uri=https%3A%2F%...
In Texas the Coroner is usually not called unless the death is suspicious in nature or the cause of death cannot be determined. I would suggest you contact the County Clerk to find out what is actually available.
Here is a link to their website: http://www.co.morris.tx.us/
Here is the address and phone number:
Morris County Courthouse
Daingerfield TX 75638
Kathie Miller Sarchet