Protection circuitry is a highly critical element in a safely usable Lithium-polymer or Lithium-ion cell. Raw (unprotected) cells are less commonly sold, i.e. many times, the manufacturer of the battery includes protection circuitry as part of the battery; however, for safety, do not assume this is the case and check the datasheet of the battery.
Purpose of Li-ion/LiPo protection circuitry
The protection circuitry serves to protect against short-circuit, over-discharge, and over-charge conditions. Loosely speaking, the circuitry relies on an over-current cutoff, an under-voltage cutoff and an over-voltage cutoff respectively for ensuring against those three conditions. Sometimes, protection circuitry also includes thermistor-based overtemperature protection.
Unprotected versus Protected batteries
You MIGHT conceivably get by with an unprotected battery, for simplicity, if you have certain components on your PCB, e.g., a fuse (prevents overcurrent/short-circuit), an undervoltage-supervisor IC (prevents overdischarge), and a smart battery-charging IC (prevents overcharge).
But my personal assessment is: Unless you are able to constantly monitor the battery, do NOT use an unprotected battery; protection circuitries are fairly simple to implement (e.g. using pre-packaged protection ICs), or alternatively, a protection-added battery is easy to purchase.
How to implement Protection circuitry (for a Two-cell pack)
If you choose to implement it yourself (versus buying a protected pack), then here are two protection ICs you can consider for your scenario (i.e. two-cell Li-ion or LiPo):
Alternatively, you could use one larger battery with one regulator. It saves power, is even easier to charge, is still regulated, and you can scale the battery to your power requirements.
You could use a boost converter with a 4.5V source, or you could use a 6V battery with a buck converter, or you could use a linear regulator such as the LM7805 for a noise free source with more power loss. If you need more than the rated 1A, there are bigger, better regulators out there for sale.
Connecting regulated outputs is always asking for trouble in my experience.
Best Answer
There are a number of LiIon charger ICs that claim to adequately manage the charging of two LiIon cells in series with no centre tap connection to the battery.
The below referenced Microchip IC is an example - their presumption seems to be that balancing for a 2sS battery is not needed.
This IC was chosen on the basis of meeting 2S spec, being in stock at Digikey and being about their cheapest offering - not always the optimum way to choose ICs :-)
The IC is the MCP73841/2/3/4 - Datasheet here.
This IC uses an external MOSFET for charging control and a 100 mV sense resistor with 100 mV drop at target current. 1A example circuits are given but a 100 mA or 10A charger could be equally well implemented.
Only claimed differences are xxx1 & 2 have thermal monitor and 3/4 do not, and 1 & 2 are for 1 x LiIon cell and 3/4 are for dual LiIon cells.
No obvious difference in general functionality is present between the 1 & 2 cell versions.
A reasonably good skim through the datasheet does not turn up any mention of cell balancing. Microchip almost always seem to 'know their stuff' - their presumption seems to be that balancing for a 2sS battery is not needed.