Simply charging a lithium battery at a constant current indefinitely is not generally safe. You need to monitor battery voltage very carefully to know when to terminate the charge. Do some research on how to charge lithium batteries safely.
Use an LTC4054LES4.2 from Linear Tech. All in one SOT package with current set by a single resistor.
Using just a resistor and you could damage the cell or cause a fire. Li-ion cells are very safe when treated well and very nasty when abused.
Maxim do the same flavour of device.
Designing your own device takes a little knowledge using constant current and constant voltage devices.
simply charging a lithium battery at a constant current indefinitely is not generally safe. You need to monitor battery voltage very carefully to know when to terminate the charge. Do some research on how to charge lithium batteries safely.