Statistically, there should have been a lot more than a couple of birthdays. Maybe up to 40 on board during a normal crossing. The Edwardians celebrated birthdays in much the same way as we would today - many happy returns, cards and presents, maybe a party (especially for children) or a night out, but most people didn't have much cash to spare so cards might be home-made, gifts often simple and practical and parties even for children were uncommon in working class homes. Some birthdays were more significant than they are now - the 21st, for instance, and the 16tn especially for a boy, because on that day he could consider himself to be a man.
Cruise ships today are well prepared for catering to special occasions like birthdays. In 1912 it might have been possible, with a word in the right ear and a tip in the right hands, to obtain a cake or other special dish for a birthday meal or a party at one of the children's sittings, and in the restaurant I daresay you could be served with whatever you were prepared to pay for. In 3rd Class the kitchen staff were probably far too busy to offer anything but the standard menu, but a steward (especially one with a greased palm) might cooperate by providing something like extra oranges or apples for a special occasion.
.