I don't know what Volt and Amp bounds are acceptable for the replacement.
Neither will anyone else that isn't familiar with the internal circuit design of the gadget.
Is it safe to change this to 9V DC 1A?
Or perhaps to 9V DC 2A?
No, it's not safe to assume that either of those will work.
In fact, even if you did find a "8V 2.6A" power adapter it might still not be safe unless you also know whether the old power adapter was regulated or not. If it's unregulated, then it's quite possible that the gadget depends on the particular behavior of the adapter, especially when charging the batteries.
Ideally you would disassemble the old power adapter and determine how smart it was - if it's regulated, or even if it has a full charging circuit inside it.
Then you would look for another adapter with those same features.
Anything else is a risky assumption.
However, without additional information, you can almost always replace one power supply with another that has the same voltage output with an equal or greater amperage output.
Given that the output voltage is not standard, though, I suspect the adapter plays a role in charging that might not be replicated by a generic adapter.
Your best bet may simply be to repair the adapter. Consider disassembling it, taking pictures, and posting here to ask for help with troubleshooting steps.