Actually its not that bad - PP3 9V batteries (the small sort) have a low current drive, perhaps 30mA is a reasonable maximum to expect from them, but the rechargeable versions are beefier (and rechargeable 
probably get 100mA or more from them.
There are larger 9V batteries available, the PP6 and PP9 for instance, often only sold as specialist flashlight batteries, and these can provide a lot more current. A set of 6 AA's provides an alternative 9V source if you can source a 6-cell battery holder.