It can be done by limiting the final voltage i.e. Run the circuit off 4.2V + Vce sat of the transistor. Cheap and dirty and prone to temperature issues. There are many single chip chargers around that cost peanuts. LTC 4054 or MAX1811 spring to mind.
You can contact these companies (Linear Tech & Maxim) and ask for samples (less than 2-3) for nothing if you can convince them you may buy more if they do the job.
The charging of a Li ion battery is first done with initial constant current, varying voltage, then when voltage is 99% of max, it switches to constant voltage, varying current. So the charging circuit is not that straight forward