Hi Mily,
You can put up birthdays of the month on the notice board. If you have a canteen, celebrate each person's birthday with a cake-cutting during breakfast in the presence of all employees. Moreover, if time permits, you can ask 1 or 2 colleagues or their seniors to say a few words about them. Such a fresh start will keep them happy for the whole day.
If you find option 1 time-consuming, there is another way. You can make a list of employees whose birthdays are in, say, May and June. On a particular day, take them out for lunch where you can chat informally, play small games, etc.
In case you find option 2 a little expensive, you can have a gathering of such employees in your own conference room instead of a hotel, with a few snacks and sweets. Conduct such gatherings monthly.
Hope this will help you.
Regards,
Vaishalee