Some advice on charging circuit used in simple UPS
If I understand you correctly, you want a charger than can switch between battery and input source (i.e. when adapter is plugged/unplugged) to power the load.  

There are plenty of charge control ICs and circuits around that can do this. The MCP73831 is a nice cheap little Li-Ion charge IC, and with the addition of a PMOS/Schottky, can switch between adapter and battery. Here is an example circuit:

  

The output is at the top right where the wire disappears (from the PMOS/Schottky)
Here is an Microchip app note which goes into some details on such a circuit.

The way it works is when the USB power (or adapter) is not present, the VUSB_IN line gets pulled to 0V by R4. This brings the gate of the PMOS (G on the symbol) to ground and turns it on (i.e. opens the Source-Drain, marked S and D) allowing the battery to power the circuit. The Schottky (marked A and K) stops the battery raising the VUSB_IN line and turning the PMOS off again.
when the adapter is plugged in, the gate is pulled to +5V and the PMOS turns off, leaving only the adapter voltage powering the circuit and letting the battery charge.