For charging I hacked a lithium battery charger circuit board with a TP4056 chip.
They are available on the Internet for a very low price.
Luckily they are easy to modify and obtain a different charging current.
In the TP4056 datasheet you can find that R4 is the resistor which determines the charging current.
On a new purchased board, you can identify the resistor by it's marking 122 (R4 = 1.2K)
Also in the datasheet you can find a formula to calculate the replacement resistor for R4:
Ibat=(Vprog/Rprog)*1200 (Vprog = 1V)
So if you use a 33K resistor for R4 you get about 36mA, that should be good. (resistor marking: 333 or 3302)
I changed the resistor, mine was 0603, that's tiny!
But this board is also available in different designs with 0805 components, making it a little easier.
When the battery is fully charged, the green LED will light up.