Perhaps I betray some ignorance about soccer leagues in respective countries, but in Canada the January cutoff is used. What cutoffs are used in other countries? If there are different cutoffs in different systems, you've made an ecological fallacy by grouping them all into the same category. The binomial seems an appropriate way to tackle the problem. P value in test for trend of 16%? You mean P value of 0.16, presumably. Logistic regression could also tell you the significance of birth month controlling for cutoff date and fraction of the total population born each month, but presumably such data would be hard to come by.