Antonyms of suddenly:
gradually, slowly, hesitantly, laggardly, leisurely, pokily, sluggishly, tardily, obviously.
Examples of usage:
  1. I looked and looked, then I called softly, but it never answered, and suddenly it was gone."
    "Spinning-Wheel Stories", Louisa May Alcott.
  2. At the time, she had suddenly gone to Paris and he had not seen her for years ...
    "The Twilight of the Souls", Louis Couperus.
  3. Suddenly Flipke the Bear came up to him.
    "Flemish Legends", Charles de Coster.