If you want to add the column in one step, you can use the rep() function. It repeats a given vector a given number of times. The repetitions can be done with the elements repeating sequentially with each element repeated n times and then the next element. Compare the output of the following two calls.
rep(c("x", "y"), 4)
rep(c("x", "y"), each = 4)
To get what you want, try
#invent a data frame
DF <- data.frame(A = 101:200)
#Make a new column
DF$k <- rep(c("x", "y"), each = 50)