The phrase "a tranquil month" is correct and usable in written English.
You can use it to describe a month characterized by peace and calmness, often in a reflective or descriptive context.
Example: "After a hectic year, I finally enjoyed a tranquil month by the seaside, free from stress and distractions."
Alternatives: "a peaceful month" or "a serene month."
After a tranquil October, November brought a return of the usual events that are part of our daily lives.
It is a tranquil September dusk and I'm only a mile-and-a-half from the centre of Woking, but the planes and their trails of pink across the sky are the only trace of the sprawling metropolis beyond.
The narrator, less extreme — perhaps less courageous? or more courageous — stays put and reaches a gentle closure, courtesy of the twins, who perform a funeral rite on a telephone switch panel made obsolete by new technology, then depart cheerfully on "a tranquil November Sunday of rare clarity shining through each and every thing".
Murray, wife of Charlton Football club chairman, Richard Murray, sat down to enjoy a leisurely start to the day on that tranquil September morning in 2000.
Duke had a similar idea in mind on a tranquil afternoon in February, as he photographed Anthime Gionet, the right-wing provocateur better known by his digital stage name, Baked Alaska.
Temperatures near 40 in New York, light winds out of the north at 5 mph to 10 mph, and wall-to-wall sunshine sound like a tranquil day — especially by February standards.
Dates written into the score signify events both great and small during the concerto's gestation, from July 1 , 2001 to Feb. 4, 2002: among them, Slobodan Milosevic's indictment, the anniversary of Jim Morrison's death, a tranquil island sojourn and the Sept. 11 attacks.
In January, in a tranquil, overgrown field dotted with olive vines and fig trees in northern Cyprus, the remains of a 56-year-old man were pulled from the bottom of a well.
Taunted by Yankees fans when the Twins played at Yankee Stadium in May, Pavano enjoys a tranquil life in Minnesota.
The Geneva-based Galerie Jan Krugier offered a tranquil 1917 neoclassical portrait of Picasso's wife-to-be, Olga.
