The Collaborative International Dictionary of English v.0.48:

Canonicate \Ca*non"i*cate\, n. [LL. canonucatus canonical: cf.
   F. canonicat.]
   The office of a canon; a canonry.
   [1913 Webster]

Moby Thesaurus II by Grady Ward, 1.0:

32 Moby Thesaurus words for "canonicate":
   abbacy, archbishopric, archdeaconry, archiepiscopacy,
   archiepiscopate, bishopdom, bishopric, canonry, cardinalship,
   chaplaincy, chaplainship, curacy, deaconry, deaconship, deanery,
   deanship, episcopacy, episcopate, pastorate, pastorship, prebend,
   prebendaryship, prelacy, prelateship, prelature, presbyterate,
   presbytery, primacy, rectorate, rectorship, vicariate, vicarship