This question is based on an erroneous assumption - that rain is never countable.
In many tropical countries the produce of the land in grain or roots, during the whole year, depends upon one rain in the spring. (Familiar Letters on Chemistry; Liebig, Justus, Freiherr von; 1843)
In the drought-disaster areas, everyone knew that one rain does not break a drought, but farmers and townsfolk alike drew a deep, fresh breath and hoped. (Rain; TIME, 1953)
But since February, most of the county has seen only two rains ,
each registering less than half an inch. (FOCUS ON DROUGHT IN THE
HEARTLAND; Jim Yardley; Atlanta Journal Constitution, 1996)
Right now, two rains into the rainy season, there's enough water
and food for the group to travel together, but just barely. (Almost
Human; Mary Roach; National Geographic, April 2008)
Since then, there have been three rains, followed instantly by prayers
of thanks. But now the dry season begins. (Echoes of the Great Dust
Bowl; Hugh, Sidey; TIME, 1996)
Though the non-count use may be the more common by far, the count use of rain seems well established, even without a modifier. In the right context, it's perfectly natural.
The meaning of rain in the above is simply a single instance of rainfall. From the American Heritage Dictionary,
a. Water condensed from atmospheric vapor and falling in drops.
b. A fall of such water; a rainstorm.