what type of degree do i need to own a nursing home?

You don't need any degree to own the home. They're kind of expensive though.

If you want to run a home then you'll need a nursing home administrator's license which you get through your state. The requirements for this license vary by state, but if you want to get hired today you'll need at least a 4 year degree, preferably even a masters in health administration or something related.

see your state's laws for this -- professional licensing division and/or medical facilities licensing.

it may be that you don't need any degree at all to own the place, but that the director thereof must have a specified set of qualifications and if you don't meet them, you must hire someone with the appropriate license.