The Collaborative International Dictionary of English v.0.48:

Propitious \Pro*pi"tious\, a. [L. propitius, perhaps originally
   a term of augury meaning, flying forward (pro) or well; cf.
   Skr. pat to fly, E. petition, feather.]
   [1913 Webster]
   1. Convenient; auspicious; favorable; kind; as, a propitious
      season; a propitious breeze.
      [1913 Webster]

   2. Hence, kind; gracious; merciful; helpful; -- said of a
      person or a divinity. --Milton.
      [1913 Webster]

            And now t' assuage the force of this new flame,
            And make thee [Love] more propitious in my need.
                                                  --Spenser.
      [1913 Webster]

   Syn: Auspicious; favorable; kind.

   Usage: Propitious, Auspicious. Auspicious (from the
          ancient idea of auspices, or omens) denotes
          "indicative of success," or "favored by incidental
          occurrences;" as, an auspicious opening; an auspicious
          event. Propitious denotes that which efficaciously
          protect us in some undertaking, speeds our exertions,
          and decides our success; as, propitious gales;
          propitious influences.
          [1913 Webster] -- Pro*pi"tious*ly, adv. --
          Pro*pi"tious*ness, n.
          [1913 Webster]

WordNet (r) 3.0 (2006):

propitiousness
    n 1: the favorable quality of strongly indicating a successful
         result [syn: auspiciousness, propitiousness] [ant:
         inauspiciousness, unpropitiousness]