I'd argue for 1919 or 1920: the flu pandemic is estimated to have killed 50-100 million people (Wikipedia), mostly in late 1918, whereas UN estimates give an average rise in world population of about 10 million a year at this point (1750 million in 1910, 1860 million in 1911)source, table 1. So we can be certain world population had dropped from 1 Jan 1918 to 1 Jan 1919, with possibly a further drop to 1 Jan 1920.

The UN publish population estimates every year from 1950 (source), and there's at least a 40M increase every year, so we can exclude that period. The only other plausible period seems to be during WWII, but you'd need something like 25-30 million excess deaths in a single year which I don't believe happened.

EDIT: I have now read the paper the estimate was based on: Johnson NP, Mueller J., . Updating the accounts: global mortality of the 1918-1920 "Spanish" influenza pandemic. Bull Hist Med. 2002 Spring;76(1):105-15. They state "in the order of 50 million" and can allow for 48-60 million deaths, but say it could be higher due to underreporting. Other estimates of the death toll have been lower, ranging from 22 million (1920s) to 30-40 million (2001). But even the lowest of these is sufficient for my argument, as at least 2/3rds of the deaths were in 1918 and the population rise you're trying to counter is safely under 15 million.

Well, from looking for long term data it seems that humans haven't had a serious decline in some time.

Population from 1750-projected 2050

Wikipedia chart from 10,000BC-2,000AD

Year to year in that chart shows some drops, but the population bounces back near immediately.

It looks like the last time growth was truly stagnate was 8,000BC-6,000BC.

Final note is the theory of the Toba Catastrophe. Some argue from the limited varitey of mitochondrial and Y-chromosome DNA that there could have been a serious population bottleneck around 70,000 years ago. The estimated number of total humans was around 10,000 at the time.

My first shot was to use the curated data of Wolfram Research to see if in recent times major catastrophes or wars resulted in negative population growth, but it appears that it was not the case. The data locates the minimum growth between 1850 and 1851 with ~1 million people. A big "dent" in growth can be seen between 1918 and 1920 as a result of the flu pointed out by /u/crb11. However it seems that the global population still rose by about 7 millions.

To look back in history is tricky, as we only have estimations and the data is aggregated in large time spans. I found a meta-study of population estimations conducted in the framework of HYDE, History Database of the Global Environment by the Netherlands Environmental Assessment Agency. The data can be downloaded here.

I plotted every series and the overall trends point to an always growing global population. However a few of the authors point to a slight decrease at around year 1400, so this would be my candidate, if at all. However bear in mind that these are some selected estimations so not everyone would agree! The result of the meta-study (HYDE 3.1) however agrees with a slight decreasing.