Answer: As worked out by parrot_knight and drplokta, the answer is Henry II, John and Richard II.
Henry II visited in 1171 and was proclaimed Lord of Ireland, a title that English kings kept until 1534. He passed the title to his youngest son John in 1177.
John visited Ireland, rather disastrously, in 1185 before he inherited the English throne, but came again with a military expedition in 1210.
Richard II came with a very large military expedition in 1394-95, and then again in 1399, but was overthrown by Henry IV while out of England and died in captivity the following year.