What does the capacity rating of the battery have to do with anything? 500 mAh tells you nothing about how much current the battery can deliver, only how long it can be expected to last at a particular current output. It is a measure of total available charge, not current.atm = at the moment
This is why i asked here for advice, how would you do to make it work?
Even with dubble 9 volt battery's the output looks the same, and a 9 volt battery got like 500mah, so it should be more then enough for this application.
So how to make it right? an op amp as a voltage follower or?
Assuming this is a typical alkaline 9 V battery, that 500 mAh rating is likely for a current draw of about 10 mA. At 250 mA, they typically fail after about half an hour (it depends on how low you can let the voltage drop for your application, but a cutoff voltage of about 7 V is pretty common for 9 V batteries).
https://www.duracell.com/wp-content/uploads/2016/03/MN1604_US_CT1.pdf

