I am unable to find a copy of the original study.
I am unable to find a reference to Tharmalingam Senthilomohan, the researcher quoted in the linked article, aside from copies of the linked article.
In the absence of such basic corroborating evidence such as the existence of the researcher, verification of his cited credentials or any scholarly reference to the study, it is difficult to take this claim seriously.
That said, further research has led to a handful of animal studies which tend to support the claim.
This study examined the effects of an extract from papaya seeds on the fertility of female rats, and found that for very high concentrations of the extract, effects could be seen on the fetus, including lower birth weight and "complete resorption of about 30% of the foetuses."
Another study looked at the effect of two compounds from a purified extract on male rats. Both were equally effective in producing, "a gradual and significant decline in cauda epididymal sperm density, percent viable spermatozoa and significant increase in sperm anomalies." The authors conclude that a "Fertility test revealed 100% efficacy."
So it seems there may be something to this after all. I wouldn't say it's been conclusively proven, as no trial or study I have found has been conducted on humans, but there is some potential here. Using the Mythbusters rating, I'd call it plausible.
A more complete list of references can be found at the bottom of this website.