I'm trying to decide how to handle multiple card outcomes in a competitive/coop survival game.

The traditional way would be to roll a d6 and consult a chart on the card. The roll determines the outcome, and this works fine but it means the outcome is based on chance.

Another Idea would be each outcome has a colour mark beside it lets say black, red, blue, white. At the start of each turn the player chooses or is assigned a number of coloured tokens and they can spend those tokens to decide the outcome of events.  This way the player is making the choice on what outcomes they receive at least initially but if they receive a number of encounters on a single turn they may have no choice but to take a bad outcome if they've already spent the tokens that would give a good outcome. (There could be a help mechanic here where another player can give them a token from their supply)

That sounds like a good idea. And as you said it leads to interaction between players as well. A player could also trade tokens with the game, such as 2 tokens for 1 token of a specific color (to be able to choose something the player think is favourable for the situation).

The token part sounds really good.

I would however use the tokens to increase the chance for an outcome.

Your players could earn/trade(great suggestion suliman) tokens ingame and spent them to increase the chance to get their result.

It still leaves a lot to chance but if a token would eliminate the chance, it will feel unfair to the other players who want a different outcome.

You can treat every option as having received one vote already to add a bit of chance for other outcomes to occur or only count voted options if you want the players to have the only control of what outcome occurs.

Increasing the chances instead of having a fixed outcome would also help if players are indecisive and let's say several pairs of players pick different outcomes (e.g. 2-2-3 which would lead to each outcome having a 29% chance but one has 43% chance instead of the outcome with 3 votes getting picked).

My suggestion would be to implement the tokens as currency and have an ingame use as well.

This way a player will have to evaluate if he uses his tokens for the current game or have a slightly better chance in the next game.