Paraguay appears to have attempted a desultory census on January 1, 1873, three years after the end of the war. What we have available is not as comprehensive as from 1886, but there are some age data. The resulting population pyramid both confirms and contradicts the data from 1886:
It confirms the data from 1886 because it also shows a giant skew in the sex ratio for the population born between 1848 and 1857; that is to say, the population aged 7 to 16 at the start of the war and 13 to 22 at its end. So far, so good.
The problem? Well, consider this table:
|1848-57 in 1872||15,083||45,567|
|1846-55 in 1886||6,420||18,697|
That is a whole lot of decline over 14 years! (57% for males, 59% for females, although the cohorts are not exactly comparable.) Is that an indication of the terrible coverage of the 1886 census? If it is, other age cohorts should experience similar declines.
|1858-72 in 1872||39,507||46,572|
|1856-76 in 1886||43,202||55,447|
|Pre-1847 in 1872||13,663||60,678|
|Pre-1846 in 1886||13,125||42,395|
They do not. In fact, given expected mortality, measurement errors and the fact that the cohorts are not equal, the 1848-57 and 1846-55 cohorts stack up remarkably well between the censuses. (The implication is that the 1886 count was a little better for that cohort.) The fit for the pre-1847 and pre-1846 cohorts is worse but still decent; it implies that men aged 25 and above were undercounted in 1872 relative to other groups because it is not possible for their numbers to have declined so little over 14 years.
The weirdness of the first cohort poses a problem. At face value, these numbers imply that something in 1872-1886 dramatically reduced the measurable population aged 15-38 while leaving other groups untouched. (15 is the youngest member of the cohort in 1872; 38 is the age of the oldest member in 1886.)
I have no idea what that could possibly be. Something that disproportionately kills prime-age adults? Unlikely. Something that makes prime age adults more desirous of avoiding the census in 1886 than they were in 1872? Paraguay was still under foreign occupation in 1872, so its possible that they distrusted their own government more than the occupation authorities. But it seems unlikely.
In short, its a mystery. It seems as though the war ripped a chunk in the fighting age male population of the country. And there is (weaker) evidence that epidemics in the late stages of the war reduced the overall population. But as for everything else the numbers seem far too unreliable to make an estimate.
As you might expect, some scholars have been there before us. A review of their evidence will be forthcoming.