If there is no pattern to the new column and no way to derive the value from an existing column, you would have to use something like the rep() function.
DF <- data.frame(Name = LETTERS[1:10])
DF$Day <- rep(c("Monday","Tuesday", "Wednesday"), c(3, 2, 5))
DF
Name Day
1 A Monday
2 B Monday
3 C Monday
4 D Tuesday
5 E Tuesday
6 F Wednesday
7 G Wednesday
8 H Wednesday
9 I Wednesday
10 J Wednesday