What does Islam say regarding some people who gather together and recite Qur'an on a specific day, for a dead person or because of building a new house, or any thing which brought happiness to them? Explain with some suggestions of Ulamah.

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

Reciting the Qur'an is one of the best deeds and most pious acts to Allah. Furthermore, it is lawful to get together for such an action since the Prophet (Sallallahu Alaihi wa Sallam) said: "Whenever a group of people assemble in one of Allah's houses (mosques) for the sake of reciting the Book of Allah (Qur'an) and studying it among themselves, they will be blessed with the decent of tranquility. Allah's Mercy spreads over them; angels surround them; and Allah mentions them in the presence of those near to Him" [Reported by Imams al-Bukhari and Muslim ].
If such people gather together for the purpose mentioned above in the Hadith, then it is legal. But, if it is meant to meet and recite collectively, then it is a form of innovation. It is also a form of innovation to specify a place, time, manner or number for such a work.
The Prophet (Sallallahu Alaihi wa Sallam) said: "Avoid invented matters (in religion), since every invented matter is Bid'ah (innovation and novelty in religion)" [ al-Tirmizi ].
Therefore, we state that the situation specified in your question constitutes a Bid'ah. But, praying to Allah to grant the reward of reciting the Qur'an to some dead is legal but without specifying a given day for that.
For more details, please read Fatwa: 82681.
Allah knows best.