One thing it's not clear is how stable the voltage has to be. Any kind of battery will slowly discharge and as a consequence the voltage will also drop.
9v batteries aren't designed for such high currents, they will discharge fast if you pull 200mA for even only one minute a day. Also, a new 9v battery will be close to 10v but as it discharges it will go down to 6-7v quite fast. If you're going to use a 9v battery you'd have to design your product accordingly.
Adapters... you say AC adapter but you probably mean DC adapters... basically the difference is the first ones output 9v AC vs 9v DC so if you want to make your product support both types you'd have to add a bridge rectifier and a capacitor in your product.
AC or DC adapters will be more regulated but may still output more than 9v when your product idles and go down to 9v during that one minute, under the 200mA load.
USB adapters are basically ac to 5v dc converters, and the majority of them will output 4.5v-5.5v and are capable of at least 400mA. Quality ones can do up to 1-2A. You can redesign your product to work directly with 4.5-5.5v or you could simply add a boost dc converter to boost the low voltage to your 9v. DC-DC boost regulators can do over 85% efficiency, so to get 9v @ 200mA, you'd pull less than 450mA from USB.
If you are going to introduce a dc-dc converter to boost voltage, you'd be better off resorting to using 2-4 AA alkaline batteries or a ~3.7v lithium battery and boost the low voltage to 9v when needed. Optionally, you could also implement charging the internal battery from usb, such charging/management chips cost under 1$ and are very simple to implement.