The Collaborative International Dictionary of English v.0.48:

Triniunity \Trin`i*u"ni*ty\, n. [See Trinity, and Unity.]
   Triunity; trinity. [Obs.]
   [1913 Webster]

         As for terms of trinity, triniunity, . . . and the
         like, they reject them as scholastic notions. --Milton.
   [1913 Webster]