With no moon, no inclination, and no seasonality, there's no reason to distinguish planetary rotation about the sun (although an elliptical orbit would still produce seasons, albeit almost unnoticeable...)
They might make "weeks" based off of digits-either five for one hand, ten for both hands, or twenty for fingers and toes. Finger/toe counting of days is always accessible, and might form their "month," but there are more useful measures.
In all likelihood, they would measure time by crop plantings (I was born thirty harvests ago) or some regular weather event. That would easily happen once they reach some agricultural milestones. From there, they begin to abstract: I will pay you in two harvest's time, this house costs two bushels every harvest cycle, etc. So "months" become some predictable harvest cycle, perhaps for grain
"Years" might be a longer growing plant's harvest cycle, such as nuts, which is expressed as a multiple of months: "There are ten wheat harvests for each nut harvest." Or it would be the time it takes for a tree to viably produce its first harvest. This would make it an important economic marker: "I will pay you back when I have my orchard grown" is expressed as "I'll pay in one tree."
So someone would say: "I am thirty nuts/trees and five wheat old."