Unfortunately, or perhaps fortunately, the times for major lifecycle events in Judaism are usually fixed. The brit milah, absent illness or unusual circumstance relating to the Shabbat and a Caesarean birth, occurs on the eighth day after birth; a funeral takes places as soon as possible after death, and almost always within a day or so.
I say “unfortunately” in this context because the range of emotions to be experienced by the family is extreme – from great joy to great sadness in just a few hours. However, I say “fortunately” also because such is life, and the capacity to fill life with happy occasions tempers even the saddest moments. I vividly recall an acquaintance of mine who, when his first son was born, immediately called his father to share with him the birth of the latter’s first grandson. As soon as he hung up the phone, the grandfather suffered a heart attack and died. He was buried the next day. The brit of the child took place in the house of mourning as the shiv’ah was concluding. The baby was named for his late grandfather.
It is not only improper to delay the brit – or the funeral; it is also unnecessary. Life always provides its moments of consolation over time – but sometimes immediately. If given the opportunity to celebrate life, we should always embrace it. That pays honor to the deceased as well as re-affirms life.
Honoring the deceased is one of the highest values in Judaism. I often comment at a house of Shiva that the people in the room are unquestionably in the most important place they could be at that particular moment. Indeed, the Talmud states the a funeral procession has "right of way" - that every other procession - gives way to the funeral procesion. There is only one exception- a wedding party. This establishes a key principle that Judaism shows great respect at a time of loss and that Judaism establishes a bias where life and joy take precedence.
The commandment to get a bris milah on the eight day is Biblical. It takes precedence even over Shabbat observance. A bris is certainly a joyous occasion, but it is also a moment of solemnity and recognition of the cycle of life. The funeral taking place later that same day will surely impact the joyous quality of the bris, but at the same time the Jewish cycle offers comfort in saying that life continues. I would urge you to find ways of honoring the deceased's memory at such a bris. It wil be on everyone's mind, and memory is a part of new life. The values and examples of the person who passed away, for example, could be offered as a hope for qualities that this new life will embody.
As to the meal that follows, there are a variety of different opinions. My suggestion is to recognize that the meal of celebration, much like the meal in a house of shiva, is much different from a party with music that would be inappropriate at a time of mourning. The direct mourners might choose to attend only the ceremony, and it would make sense to plan something in a month or so to celebrate more fully.
First and most important: If this is in reference to a particular and/or individual situation, please confer with your Rabbi to receive the most authoritative guidance for you. However, for the sake of general discussion and edification, here is my response:
One’s obligation to perform brit milah on the eighth day supersedes many mitzvot, including Shabbat. If a child is scheduled to be circumcised on the eighth day of life, and there happens to be an intervening death and funeral, the brit milah still happens on the eighth day. The rituals of the brit milah – the circumcision itself, the roles of father and mother, sandek, k’vaterin, etc – must be performed as needed, but see below regarding the state of mind and the meal that follows.
One may defer a brit milah but only for medical purposes. In that vein, the higher mitzvah, of course, is pikuach nefesh – the preserving of life – and therefore if the child is not ready for circumcision, then it is deferred until his doctor declares him fit.
The question about which authorities have ruled is whether one can “celebrate” the brit milah, which is understood to be attending the meal that follows. If the brit milah happens to be scheduled for the day of the funeral or the period of shivah – the first seven days of mourning after the burial – it is recommended that a mourner not attend the meal of celebration of the brit milah even though s/he may (some may say ‘should’) attend the circumcision ceremony.
So to review, the celebration is something that is deferred until after shloshim – the thirty day period of mourning – but the brit milah goes as scheduled on the eighth day, even including the parents, mohel, and others involved in it.