Technoligically, the world has gun powder (which could be used somehow to fuel a tank, I'd think).
Someone correct me if I'm wrong, but gunpowder (and its derivatives) don't make particularly good fuel, save perhaps as propellent for projectiles. It's explosive nature can't drive a mechanism in the same way that coal can drive a steam engine: You might be able to blast something out the back of a tank for a quick boost, but as a normal fuel, it's just too dangerous (and not reliable enough) to work.
There's also the possibility of a tick-tock tank/clockwork tank...
Like a wind up? It will suffer in speed and (probably) a naturally overcomplicated mechanism. The more moving parts you have, the more moving parts you have to break. Further, someone has to wind it, which means when the "charge" runs out, your tank is essentially useless on the field.
I think your best option is to have someone discover the steam engine (which would be quite a leap) or have something that works more like a golem - something that doesn't need any actual fuel or mechanism to "go." I'd imagine something like this might look more like a walker from Star Wars than it would a tank as we see them, today.
Lastly, there comes the question of why would you develop a tank in particular? We recognize them as warmachines because of their commonality on modern battlefields, but they were initially used as a counter to trench warfare - and developed as such. rather than sending a bunch of unarmored boys across no man's land to take the enemy trench, a tank could rumble across without having to worry as much about small arms fire: the technology first saw real use in the real world in the First World War.
Now, there's no reason you need to use the same logic in justifying their development - but why tanks?
Interesting question!