A month of Sundays is easy to work out — 28-31 Sundays or 190-211 days elapsed.
A blue moon is somewhat harder, complicated by the fact that the definition appears to have changed. The modern definition, however, is "the second full moon in the same month". Full moons occur approximately 29.5 days apart (however, due to irregularities in the moon's orbit this figure varies), and fortunately for me Wikipedia have found the answer for me and Blue Moons occur on average every 2.72 years, or just under once a 1000 days. Thanks to February only having 28 days, though, the shortest time between two Blue Moons is two moons (second Full Moon in January and then second in March, with none in February), which will next occur in 2018.
All in all, something that won't happen in a month of Sundays may still be more frequent than something that happens once in a Blue Moon.