So this is a difficult question to answer for the very reason you point out - there are no statistically sound sources that can give us firm population estimates. The majority of the information is derived from estimates of household size multiplied by the number of families in the tax records for small localities and then extrapolated over the whole of the island (Petty, The Political Anatomy of Ireland, 1691; Cullen, "Population Trends in Seventeenth-Century Ireland", Economic and Social Review, 6 (1975), pp. 149-65; idem, "The Irish Diaspora" in Canny, Europeans on the Move).

Lenihan's essay "War and Population, 1649-1652" (Irish Economic and Social History, Vol. 24 (1997), pp. 1-21) presents a thorough criticism of the numbers Petty and Cullen arrived at. Through his analysis, Lenihan is able to demonstrate that Ireland went from a population of about 1 million in 1600, to about 1.5-1.6 million in 1649. This coincides with the average rate of growth found by R. A. Houston in his Population History of Britain and Ireland, where between 1600 and 1687, the population of Ireland increased at an average rate of 0.8% per annum, starting at 1 million in 1600 (the numbers are not perfectly aligned, but higher rates of migration from England and Scotland to Ireland after 1640 make up for the difference. See essays on England and Scotland in Canny, Europeans on the Move).

Based on a regression from an estimated population in 1672, Lenihan argues that between 15-20% of the population of Ireland died between 1649-1652. This puts the rough estimate of dead from war, disease, and famine at 300,000 people (Gentiles, The English Revolution and the Wars in the Three Kingdoms, table 15.1). The resulting estimate of the Irish population in 1652 would be about 1.3 million, and the population would have recovered for the most part in 1672 with a population of 1.5 million.

It is important to note that the above are all rough estimates based on projections backwards and forwards from rougher still estimates of local communities in Ulster, Dublin and more rural counties. Still, the estimate that about 300,000 people died due to the Cromwellian conquest is not likely to decrease, and may be an underestimate.