This report discusses the use of small cryogenic coolers for cooling the Muon Ionization Cooling Experiment (MICE) liquid cryogen absorbers. Since the absorber must be able contain liquid helium as well liquid hydrogen, the characteristics of the available 4.2 K coolers are used here. The issues associated with connecting two-stage coolers to liquid absorbers are discussed. The projected heat flows into an absorber and the cooldown of the absorbers using the cooler are presented. The warm-up of the absorber is discussed. Special hydrogen safety issues that may result from the use of a cooler on the absorbers are also discussed.