There have been a couple that used J79 engines.
Breedlove used one in one of his Spirirt of Americas.
Art Arfon's Green Monster used a J79.
There was a more current project built from an F104 (part) fuselage.
The North American Eagle.
I think that project dried up a few years back.
They had hoped to break the Thrust SSC record.
...
I am wrong.
I guess the project is still alive.
Here it is:
http://www.landspeed.com/