My kit uses a 1.5A 7809. BTW- it states that fact.
I said it requires a higher input, 18V, because without a higher input it would not reach an output voltage high enough to calibrate a controller to where most people want them set.
The main problem with charging a tiny battery like that (0.280 ah) will be limiting the charging current. Do not want to just send 1.5A into it.
A couple small power resistors can fix that problem.
Another problem is you do NOT have a '9V battery'.
What is the "real" voltage of the "9V" battery? It depends. But it is not 9.0V.
There are several versions, and several sub-versions. Mainly and basically, 7.2V, 8.4V, and 9.6V nominal. With a simple charging system, they would be charged to about 8.4V, 9.8V, and 11.2V.
Of those, most common is the 7.2V. It has 6 nicd or nimh cells.
Considering it would want charged to no more than 8.4V, a simple system using a 7809 will not work because they can not be adjusted below 9.0V.
You could use the schematic for my kit, but use a 7806 instead of a 7809.
Still need to regulate the max charging current.
I would try to limit it to 10% (28ma), and consider it a 12~16 hour charger.
Pre-coffee guestimate: My circuit, with a 7806 instead of 7809, and a 180 ohm 1/4W resistor in the power supply wire (between the 13.8V and circuit positive input).
There are many ways to skin a cat.
G-