The principal aspect for a battery charger is the current, that is because the voltage in the different stages of charge will be diferent.
So you need a constant current source.
And you already have a 9Vdc. So you need the current. There are two ways to solve that.
Using the LM317 as a current source you can have a good information in the web page of onsemi. This is the very easy way.
The second is using a MOSFET, like the IRFD110, as a current source. Information is available everywhere the Vgs = 4.8322 will give you the Id=0.7 Amp.