How many of those uniquely dangerous old world diseases were even around before 146 BC? The eastern hemisphere's advantages in disease creation- domesticated animals, big cities, dense trade routes- took a while to get rolling.
And even then, it'd have to be something that that specific Carthaginian ship had on board. With Columbus it was a lot more people, a lot later, and a lot more times.
Typhus existed in epidemic form and could have life long asymptomatic carriers so that is a good option for one. Tuberculosis is another option that was around and has long lived asymptomatic carriers. With TB most people infected with it actually are asymptomatic carriers that can turn infection at any time. As for how likely... hell if I know. If I had a good handle on the percentages I could be getting a paper in Nature about historical epidemiology. I'm just trying to give an option that is possible and would actually have an effect beyond some weird guys show up on a boat half starved and just become a weird story people tell after a few hundred years.