The beta distribution is conjugate prior for the binomial distribution.
Is the beta-binomial distribution a conjugate prior for some sampling distribution?
You're looking for the hypergeometric distribution. Incidentally, this link is one of the first two hits on Google for
"beta binomial" "conjugate prior".
Have a look at the wikipedia page, there's a very nice conjugate prior table there.
If you are working with
python, you can import the conjugate_prior package and start hacking
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