Based on the Islamic text Riyaz-u-Salatin, date of Mahabharata war may be estimated to be to 2865 B.C.E
The history book Riyazu-S-Salatin, by Ghulam Hussain Salim (~1785 C.E), which is held in very high esteem by members of a certain community, and which is primarily concerned with the Islamic history of Bengal (West Bengal and Islamic Bangladesh) however also discusses the pre-Mohammedan history of Bengal in some detail.
The pre-Islamic royal history of Bengal has been described by Shri Ghulam Salim thus:
a. Raja Bhagirat of the Khatri tribe, who sided with Duryodhana in the Mahabharata War and got killed. As per Shri Ghulam Salim, Bhagirat apparently ruled for (an absurdly long) 250 years !
b. After this his 23 descendants ruled for 2200 years - implying improbably long average reigns of 96 years!
c. Then it was the Kayastha Noj Gouriah / Bhoj Gauirah family who took control of Bengal. He and his 8 descendants ruled for 250 years. Now suddenly we have an average reign of 28 years down from 96 years above.
d. Then adiśura and his 11 descendants ruled from 714 years, for an average of 60 years of reign.
e. Then it was Bhupal Kayasta and his 10 descendants who ruled for 698 years, that is an average of 64 years.
f. Then Sukhasena Kayasta and his seven descendants ruled for 160 years, 20 years average reign.
That means these 61 persons ruled for 4272 years.
g. Then came sukh sena of the Bodo caste who ruled for 3 years.
h. And then came Vallala sena - who apparently came 4025 years after the Mahabharata war.
Now Vallala sena, as we know from standard history texts, ascended the throne in 1160 C.E - so as per the Islamic text Riyaz-u-Salatin, the date of mahabharata war happened in 2865 B.C.E
1. Even a cursory reading of the relevant section of Riyazu-S-Salatin would convince one as to the utter absurdity of the claims of the author [Shri Ghulam Hussain Slaim], his complete lack of historical sense and his penchant of documenting myths and legends which he passes of as history [ with respect to this section].
2. Scientific methods/ archaeology/ concepts of historiography do not seem to be important to the author - thus we find Bhagirath ruling for 250 years, which is biologically impossible.
3. The author being an orthodox follower of his faith had a deep rooted and almost missionary dislike for Hindus and anything Hindu (like idol worship, fire worship etc and proceeds to verbally disparage the practice of the Hindus) - and his religious bias is apparent as one reads through the text.
4. And there is always the matter of things getting lost on translation - the original work was in Persian and later translated to English by Abdus Salam which I have used for my notes.
Riyazu-S-Salatin (A History of Bengal) by Ghulam Hussain Salim 
Translated by Abdus Salam Under the Auspices of: Idatrah-i Adabiyat-i Delli and Published by: Mohammad Ahmad