Is it permissible to bury the deceased in his house?

Firstly: 

The Sunnah is to bury the dead in public graveyards. 

Ibn Qudaamah (may Allah have mercy on him) said: Burial in
Muslim graveyards was more liked by Abu ‘Abdullah [i.e., Imam Ahmad] than
burial in people’s homes, because it is less harmful to the living among his
heirs, and is more befitting, and it means that there will be more du‘aa’s
and prayers for mercy for the deceased. The Sahaabah and Taabi‘een, and
those who followed them, continued to bury their dead outside the city. 

If it is said: The Prophet (blessings and peace of Allah be
upon him) was buried in his house and his two Companions were buried beside
him, the response is: ‘Aa’ishah said: “That was only done lest his grave be
taken as a place of worship.” Narrated by al-Bukhaari. 

And because the Prophet (blessings and peace of Allah be upon
him) used to bury his Companions in al-Baqee‘, doing so is better than doing
otherwise. 

With regard to his Companions, they regarded this as
something that applied only to him, and it was narrated that “The Prophets
are buried where they die.” And it was to protect his grave and to
distinguish it from others.

End quote from al-Mughni, 2/193 

But… If it is not possible to bury a Muslim in the graveyard
and there is no place to bury him other than in his house, then there is
nothing wrong with that. 

An-Nawawi (may Allah have mercy on him) said: It is
permissible to bury the deceased in his house or in the graveyard, but the
graveyard is preferable according to scholarly consensus. 

End quote from Sharh al-Muhadhdhab, 5/245 

You have to speak to the officials in your country about
setting aside some land for burying the dead, or you can advise some good
people to buy some land and set it aside as a waqf for burial of the dead,
or let the people come together to buy it. That is because widespread burial
of the dead in houses will reduce the space available for the occupants and
it may lead to disrespectful treatment of the graves. 

And Allah knows best.