I don't have two children with birthdays in the same month. However, if I let baby-under-construction arrive in its own time, I almost certainly would. For a variety of reasons, I'm having a scheduled section at 40 weeks. That will be June 29th. If I waited for labour, it's almost certain (based on my previous pregnancies) that it would be at least another week and a half. That would put him in July, with ds2.
While we don't have birthday in the same month, once baby-under-construction arrives, the birthdays of my living children will be:
My birthday is also in June, so every birthday in our family, except dh's, occurs in the space of just over four months. From ds1's to dh's is almost exactly six months, and then we have six months with no birthdays at all (except our angel, Aaron, who was stillborn in November).
The possible proximity of b-u-c's birthday and ds2 was not planned at all, and neither was the grouping of birthdays. I'd honestly prefer a little more spacing. However, I long since gave up on planning my reproductive life.