The Collaborative International Dictionary of English v.0.48:

Papacy \Pa"pa*cy\, n. [LL. papatia, fr. L. papa a father,
   bishop. See Pope.]
   1. The office and dignity of the pope, or pontiff, of Rome;
      papal jurisdiction.
      [1913 Webster]

   2. The popes, collectively; the succession of popes.
      [1913 Webster]

   3. The Roman Catholic religion; -- commonly used by the
      opponents of the Roman Catholics in disparagement or in an
      opprobrious sense.
      [1913 Webster]

WordNet (r) 3.0 (2006):

papacy
    n 1: the government of the Roman Catholic Church [syn: papacy,
         pontificate]

Moby Thesaurus II by Grady Ward, 1.0:

88 Moby Thesaurus words for "papacy":
   Apostolic See, See of Rome, aedileship, archbishopric,
   archiepiscopacy, archiepiscopate, aristocracy, bishopric,
   chairmanship, chancellery, chancellorate, chancellorship, chiefery,
   chiefry, chieftaincy, chieftainry, chieftainship, consulate,
   consulship, deanery, dictatorship, dictature, directorship,
   emirate, episcopacy, governorship, headship, hegemony, hierarchy,
   leadership, lordship, magistracy, magistrateship, magistrature,
   masterdom, mastership, mastery, mayoralty, mayorship,
   metropolitanate, metropolitanship, nobility, papality, pashadom,
   pashalic, patriarchate, patriarchy, pontificality, pontificate,
   popedom, popehood, popeship, prefectship, prefecture, premiership,
   presidency, presidentship, prime-ministership, prime-ministry,
   princedom, princeship, principality, proconsulate, proconsulship,
   protectorate, protectorship, provostry, provostship, rectorate,
   rectorship, regency, regentship, ruling class, seigniory,
   seneschalship, seneschalsy, sheikhdom, sheriffalty, sheriffcy,
   sheriffdom, shrievalty, supervisorship, suzerainship, suzerainty,
   the Vatican, tribunate, vizierate, viziership