On the web I can find many occurrences of both 色々な and 色々の.
色々な seems to be used more often though.
Can I always use 色々な and get away with it, or is 色々の the only choice in some particular cases?
If yes, which cases?
This is where the status of a word is murky. It is unsettled between a na-adjective and a noun. However, probably most of the cases where you found "色色の" come from some old people. It has an archaic flavour. In addition, "色色" does not take any other case markers in present-day oridinary conversation like: "色色が" or "色色を"; it should not allow genitive "の" as well (but according to the link Tsuyosi Ito provided, there are cases where it may be used). You can always use "色色な", and get away with "色色の".
Addition: Tsuyoshi Ito's link below reminded me of another similar example: "様様な" vs. "様様の". The contrast between them can be considered the same as above.