The Colecovision is notorious for having an oversized power and a not-so reliable power supply.

Here are a few solution(s) (I'll add more as they come) for replacing the power supply in this old console.

The first one (and only one) is the ColUSB, this takes basically a cell phone charger with at least 2 Amps of power, and a USC-C connector and this little device to give new, clean and reliable power to the console.

Glen from "Glen's Retro Show" has done a review.  Check it out.

UPDATE: This solution appears to be out of stock everywhere.

The second is a more involved and a less "Plug and Play" solution.
This particular solution has not been entirely originated by Ikrananka, but he documented it the best.
Check out this thread for an awesome job by him.