Try:
df[, cols <- grep("^DATE", names(df))] <- lapply(df[, cols <- grep("^DATE", names(df))], as.Date, format = "%y%m%d")
Example:
df <- data.frame(DATE1 = c('910812', '900928'), DATE2 = c('890813', '890910'))
# Apply the above and you get:
# > df
# DATE1 DATE2
# 1 1991-08-12 1989-08-13
# 2 1990-09-28 1989-09-10
# > class(df[, 1])
# [1] "Date"