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]

The Devil's Dictionary (1881-1906):

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