If, as I suspect from the context, the samples aren't huge, then this issue is not so straightforward. This article summarizes some of the issues involved, and includes many references. It ends by recommending the score method of Miettinen and Nurminen, but bear in mind that one of the authors of the paper is Nurminen.
Another very useful reference is Brown, Cai & DasGupta (2001). They write (in the abstract):
Based on this analysis, we recommend the Wilson interval or the
equal-tailed Jeffreys prior interval for small n and the interval
suggested in Agresti and Coull for larger n. We also provide an
additional frequentist justification for use of the Jeffreys interval.
and note that the coverage of the standard methods is often bad, even when N is large, and that (very unusually) there is not a monotonic relationship between the coverage and the sample size (that is, larger samples can be "worse" than smaller ones).
For looking at a single binomial proportion, a good article is Agresti, 1998. This may be useful background for the other two articles, which are more directly on point for your question.