I think you can get to around 5/8 wins by having this system:

Designate one color even (say, red), and one color odd. Every turn, you put down the color of card of your turn. For the flip card, if it is your color, pick that; otherwise, pick the other card.

There is the chance of the top card being the same color, but about 50% chance of it not. And if they pick your card, it's the right color. The way this starts to break down is when you run out of cards of a color. I suppose you could have a system where when you run out of cards of a certain color, you know that color will be used for the next 4 tricks.

I think you can get to around 3/4 wins by having this system:

Designate one color even (say, red), and one color odd. Every turn, you put down the color of card of your turn. For the flip card, if it is your color, pick that; otherwise, pick the other card.

There is the chance of the top card being the same color, but about 50% chance of it not. And if they pick your card, it's the right color. The way this starts to break down is when you run out of cards of a color. I suppose you could have a system where when you run out of cards of a certain color, you know that color will be used for the next 4 tricks.