We will design a charger circuit with commercially available components to your requirements. The battery size for this type of application should be something in the 100 mA-Hr range more or less.
Deliverable: BOM with the part number for all parts selected. Schematic describing the circuit that gets closest to your requirements, or exceeds your requirements. Estimated performance wherever possible and reasonable.
Note: If you choose the fuel gauge circuit design option we will deliver BOM, and schematic similar to what is described for the charger. Please make sure to include your requirements for the fuel gauge too.