How can I make a 9V 1A DC adaptor to power this audio mixer?
You appear to be asking for a (rechargeable) battery power pack for mobile use.
Note that your mixer is highly unlikely to draw 1A from it's power inlet. I'd measure the current draw. It'll most likely be less than 100mA. The 1A A.C. supply is simply used for convenience. There's little demand for 1 watt AC adaptors.
Similarly, it's unlikely that exactly 9 volts is required. So that the power pack is still useful until exhausted, I'd go for a 12V power pack when freshly charged.
Another possibility is qty 3 18650 Li-ion batteries. Again 2500mAh is a common capacity for these.
So, what batteries to use ? A bunch of NiMH AA batteries in series may be practical. The open circuit voltage of NiMH is ~ 1.3V. 10 in series gives 13V when fresh, 8 in series gives 10.4V. Your choice. The Ah rating depends on the batteries but 2500mAh is readily available, giving you 25 hours use at 100mA current draw.
You'll find no shortage of holders for AA batteries on ebay for example. You simply need to package them in a suitable enclosure, aka a 'plastic box !
I'd recommend fitting a large electrolytic capacitor 'across' the output btw to ensure low AC output impedance at audio frequencies. Say 4700uF 16V.
A 'low battery' warning LED might be a good idea too. Simple to design. If you want, I'll draw one.
You'll need a charger of course too.