What battery would you like to use? 3 AAs in series would work, 4 if you use rechargeable Ni-cads. A single Li-ion battery (3.7V nominal) would probably work, but as it discharges your power amp might not be happy (data sheet says 3.6V minimum). A sealed lead-acid (SLA) at 4.5V would work. There are lots of options since your two devices overlap in the 3.6-5V range.I need help For wiring yhis two circuits with the same battery.
He needs something in that range. No idea of any other criteria such as size, capacity, cost, weight, rechargeability, whatever.... your two devices overlap in the 3.6-5V range.