You are not a million miles away with your estimate.
BUT you need to think about what your device is going to be doing to make a real estimate. Use your calculations of:
500mAh / 59mA = 8.47h if your device is only going to be used as a receiver.
Or use the higher value of:
500mAh / 278mA = 1.8h if the device is going to be used as a transmitter.
But you may want to take some other possibilities into your calculations, if you dont need to device actually doing anything for some of the time, you can use the hibernate mode on the device. The current consumption in this mode is 4uA. So if your device lived in this hibernation mode for the whole of its life cycle:
500mAh / 0.004mA = 125,000h or 14 years...
but in general the low power deep sleep is 250uA so:
500mAh / 0.25mA = 2000h so a measly 8.3 days.
One other consideration is the battery life itself, when you look at datasheets, the battery capacity changes with the discharge current. For instance, in this datasheet, at 300mA discharge, the battery has just under 400mAh of capacity, a reduction of 20% from your calculations! but at 25mA, the battery could last over 600mAh, an increase of over 20% from your calculations.
One final thing to consider is that your device doesn't run at 9v, it runs at 3. This means that you need to do some trickery with the voltage. If you want to use regulator, you will instantly reduce your battery life by 60% due to current losses. Another way is to look into buck converters, where you could get a decent efficiency, you might only lose 20% of the battery life. The final consideration would be to change the batteries; if you were to use AA batteries, not only would you increase battery life (much higher mAh rating), you wouldn't get the same losses related to regulation because the voltage would already be lower.
Also, have you thought about using multiple chips instead of a single chip solution? may be easier to quantise current draw for each part. Just a thought