The Collaborative International Dictionary of English v.0.48:

Presidency \Pres"i*den*cy\, n.; pl. Presidencies. [Cf. F.
   pr['e]sidence.]
   1. The function or condition of one who presides;
      superintendence; control and care.
      [1913 Webster]

   2. The office of president; as, Washington was elected to the
      presidency.
      [1913 Webster]

   3. The term during which a president holds his office; as,
      during the presidency of Madison.
      [1913 Webster]

   4. One of the three great divisions of British India, the
      Bengal, Madras, and Bombay Presidencies, each of which had
      a council of which its governor was president.
      [1913 Webster]

WordNet (r) 3.0 (2006):

presidency
    n 1: the tenure of a president; "things were quiet during the
         Eisenhower administration" [syn: presidency,
         presidential term, administration]
    2: the office and function of president; "Andrew Jackson
       expanded the power of the presidency beyond what was
       customary before his time" [syn: presidency,
       presidentship]

Moby Thesaurus II by Grady Ward, 1.0:

133 Moby Thesaurus words for "presidency":
   acme, aedileship, archbishopric, archiepiscopacy, archiepiscopate,
   aristocracy, authority, authorization, be-all and end-all,
   bishopric, blue ribbon, captainship, chairmanship, championship,
   chancellery, chancellorate, chancellorship, chiefery, chiefry,
   chieftaincy, chieftainry, chieftainship, command, consulate,
   consulship, control, convenership, custody, deanery, dictatorship,
   dictature, directorate, directorship, dominion, effectiveness,
   emirate, episcopacy, first place, first prize, foremanship,
   generalship, governorship, guardianship, headship, hegemony,
   height, hierarchy, highest, imperium, influence, intendancy,
   jurisdiction, kingship, leadership, lordship, magistracy,
   magistrateship, magistrature, management, managership, masterdom,
   mastership, mastery, maximum, mayoralty, mayorship,
   metropolitanate, metropolitanship, most, ne plus ultra, new high,
   nobility, overseership, palms, papacy, paramountcy, pashadom,
   pashalic, patriarchate, patriarchy, pontificality, pontificate,
   popedom, popehood, popeship, power, prefectship, prefecture,
   premiership, presidentship, primacy, prime-ministership,
   prime-ministry, princedom, princeship, principality, proconsulate,
   proconsulship, proctorship, protectorate, protectorship, provostry,
   provostship, record, rectorate, rectorship, regency, regentship,
   rule, ruling class, say, seigniory, seneschalship, seneschalsy,
   sheikhdom, sheriffalty, sheriffcy, sheriffdom, shrievalty,
   sovereignty, stewardship, superintendence, superintendency,
   supervisorship, supremacy, suzerainship, suzerainty, sway,
   top spot, tribunate, vizierate, viziership, zenith



The Devil's Dictionary (1881-1906):

PRESIDENCY, n.  The greased pig in the field game of American
politics.