We stayed in Jeju Landing Shinhwa hotel (under Marriott), they provided us with baby cot.. You must request when book and email them again to remind them and upon check-in.. But still, subject to available..
Just got back from a 2weeks trip to Korea(Seoul/Jeju) with my 8mths old. No cribs, so I booked a family room instead. One that has a Queen + single bed, so I can co-sleep with my baby & my hubb in the other.
I just went to Jeju over the CNY period and Ocean Suites Jeju Hotel provided a baby cot for my 1 year old baby. Hope this helped!
be prepared to co-sleep for that period