9v AC 2000mA power adaptor for a 9v AC 1000mA device
Yes, that's fine.
The voltage matches (important point #1), and the adapter can deliver 1000 mA or more (important point #2).

The current rating for a power adapter says how much it can provide; how much it actually does provide is up to the load.
In other words, any adapter that is 9 V and 1000+ mA should work just fine.