ZDV Center Controller reported their sector was assigned responsibility for underlying TRACON airspace which could not open due to staffing. The Center Controllers had not been trained on procedures or techniques to work air traffic in that airspace.

Narrative

On Day 0; at XA:00 COS TRACON/Tower informed ZDV that they will not be able to keep the TRACON open today due to staffing. ZDV - Area 3 - 41R would be assuming the COS airspace in approximately 20 minutes; while COS Tower would remain open and revert to a VFR Tower. This is an operation that Area 3 has not been properly trained on and never works. An adequate briefing on these contingency procedures has never occurred; and no one in Area 3 is proficient on the operation; which is a major safety concerned. Lab problems [simulated training scenarios] have been requested on COS Tower only operations for the last five years; but they have been repeatedly ignored. A last-minute closure of COS TRACON; with the assumption that Area 3 will be able to accommodate assuming the airspace; on a beautiful VFR Saturday; while ZDV is already hitting record traffic counts consistently with less CPC's than ever; adds unnecessary stress to the already overworked and fatigued controllers and is an unacceptable risk to the NAS.Recommendation: More Training for Area; to prepare us for the next time we have to take COS airspace.