How do I make a circuit that charges two 3.7 Li-Ion batteries (in series) with a 5v input?
Yes, you can charge your batteries with the 5 volts.

1) You would need a boost converter to boost the 5 volts up to the voltage needed to charge the batteries, which would eventually be 8.4 volts.

2) You will need a constant current/constant voltage power charger so that the batteries are charged correctly,

3) Lithium batteries in series need to balanced if they are charged in series.  This means that you need to add a battery management chip to your charger that will balance the voltage of the batteries, and make sure that the batteries are not over charged or under charged - very important.  Lithium ion will catch on fire or worse if not managed properly.

4) It might be easier to have a boost converter and ONE lithium ion battery and just boost the voltage of that battery to what your watch needs.  It would make the charging of the battery easier.  Of course you would need to find a battery of sufficient capacity.

Good luck