Name a common greenhouse gas containing only hydrogen and oxygen

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.