The common greenhouse gas containing only hydrogen and oxygen is H2O, this is water vapor.
The common greenhouse gases are water vapor, carbon dioxide, methane, nitrous oxide and ozone.
The composition (chemical formula) of those gases are:
Water vapor: H2O
Carbon dioxide: CO2
Methane: CH4
Nitrous oxide: NO
Ozone: O3.
As you see the only one of those that contains only hydrogen and oxygen is H2O, water vapor.