No. Only a recognized CBO can apply for a FRIA.
However a CBO can apply for an off-site sanctioned event but that 'event' is not permanent. For years AMA events that are too big for club (FRIA) fields have been held at places like Airports, Private properties such as ranches, and even Polo fields to name a few.
But those off site events are ran by a sponsoring club under the strict guidelines of the CBO. This list of requirements is large and you can read about them on the FAA's website.
It should suffice to say there is no way that you could turn your ranch into your own private "FRIA", nor would you be able to have an event sponsored in which allows only you to fly around at anytime you like.
On the other hand, there are always AMA (CBO) clubs in search of a new flying site. I've been a member of AMA over 45 years and ALL of the clubs I was a member of, at some point or another, discussed finding a new or better flying site. But you as an owner of the property must understand what comes with that. A designated part of your land will be run and managed by the club at all times according to the CBO.
But also that club would have to abide by whatever rules you as a property owner wishes to negotiate. For instance you could say that you only want them active for a few days a week, or even only six months out of the year as an example, and if they agree then that will be the periods they apply for and that field would ONLY be considered a FRIA during those times when the club is active
Also, to even fly at a club located on your own property you would still have to be an AMA member and follow club and CBO rules and keep in mind, your allowing all of the members unfettered access to that flying site.
If thats what your after, reach out to the AMA and find all the clubs near you and send them a letter that you have a large property and may entertain having a club set up a flying site.