I found this schematic, do you think this will work?
We're getting closer, good.
But dude, that's way too small for me to see what's really happening. In principle some of the scheme looks fine, but the devil's in the details, which no person could possibly parse at this magnification. Please post the source URL for your diagram.
In your little drawing, it looks like an astable oscillator is providing pulses to the counter via two pushbuttons, up and down. That's a bad way to go for several reasons, 1) the switches will bounce causing your count to be all over the place, and 2) depending on when the user hits the switch the clock edge could be at a bad place, again causing a weird count. Plus I can't tell what the two NAND gates between the clock and pushbuttons are supposed to be doing; it looks like gibberish...
What's your clock rate? It looks like maybe 2Hz, which means it's not really useful (it's slow). In your implementation the user must hold the button down until the correct count is reached, which could get old at that rate. Why not have the user punch the button the requisite number of times to get to the proper score? That's easier to implement, too. Drop the clock, and debounce two pushbuttons, each driving the up/down pins. You ought to add a reset button too, to clear the score.
A clock with somewhat higher rate might be useful in getting the score to some intermediately high value, say 50, without tiring the user by pushing buttons, too.
Think these things through. Then you can make it happen...