During the Salyut 1 mission, the birthday of one of the cosmonauts was celebrated with a very small amount of alcohol, as far as I have read.
The first alcoholic drink went to space in 1971, destined for the Salyut-7 [presumably a typo, as the Salyut actually in orbit at the time was Salyut 1; Salyut 7 didn't fly until 1982] orbital station. One of the cosmonaut's birthday [sic] occurred while he was in orbit, and friends gave a present before launch: they hid a bottle of Armenian cognac in the wristband used for measuring blood pressure.
The cosmonaut in question was presumably Viktor Patsayev, who turned 38 on board Salyut 1 (Soyuz 11, the only mission to successfully harddock with Salyut 1 and have crew enter the station, docked with Salyut 1 on 7 June 1971 and undocked on 29 June; Patsayev's birthday was on 19 June).
This source (in Russian) claims that Lev Denisov revealed that ground workers did hide the bottle of cognac, for Patsayev's birthday celebration:
Рабочие, готовившие корабль «Союз-11» к старту и устанавливающие на него «научную аппаратуру», рассказали Денисову, что во время полёта на орбиту у одного из членов экипажа, Виктора Пацаева, будет день рождения, и предложили сделать ему подарок в виде бутылки армянского коньяка. Они даже выбрали на борту место для тайника, спрятав бутылку за манжетами для измерения кровяного давления. Денисов согласился и лично проконтролировал, чтобы никто из инспекторов не нашёл заначку. Космонавтам сообщили о бутылке, уже когда те были на орбите.
The workers, preparing the Soyuz-11 spacecraft for launch and installing “scientific equipment” on it, told Denisov that one of the crew members, Viktor Patsayev, would have a birthday during an orbit, and offered to give him a gift in the form of a bottle of Armenian cognac. They even chose a hiding place on board, hiding the bottle behind the cuffs for measuring blood pressure. Denisov agreed and personally controlled so that none of the inspectors found a stash. The astronauts were informed about the bottle when they were in orbit.