slowly, gradually

(だんだん) Gradually, little by little.   $$$
しずつ(すこしずつ) Same as だんだん
じょじょ Step by step – improving your skills at Japanese, say, or learning something one technique at a time.
(しだいに) Over the course of time; as time passes. Unlike the others, 次代 is limited to things that are not intentional.  You can use 次代 about nature (as time passed, the hill eroded away) or about yourself (over the course of time my grief of my Mother’s death lessened). Careful, though: if it has a に after it like this: 次代に, then it has an entirely different meaning: ‘it depends on’ (more similar to によって).