How much benadryl (diphenhydramine) and beer would knock you out completely?

Depends: That depends on several factors: your tolerance to alcohol, your sensitivity to antihistamines, your present level of sleepiness, whether or not you've ingested any stimulants, etc. I assume you're looking to a benadryl/alcohol combination to help you sleep? If so, that is a bad idea. The resulting sleep quality would be terrible, and you'd awaken feeling unrested (or worse!) talk to your doc.