To use Cohen's D, you're going to need some sort of standard deviation info. However, it is possible that you could estimate the standard deviation, if you assume that your distribution is normal. This means that your data isn't skewed towards one direction or the other.

If this is the case, then you can use the formula

standard deviation estimate = (largest possible value - smallest possible value) / 6

This is not as reliable, but it could be used as an estimate. Note that you could divide by 4 too, and it would yield a more conservative estimate.