I gave Mysore a shot once, though didn't give it very long. I admit I chose them mostly because of their primary culture - the idea of making most of North America Kannada appealed to me.
Jokes aside, they play much like French vassals but in a worse tech group. The start is very slow, just remain their vassal while building up an economy and improve their sliders. Eventually, India will probably end up split in a three-way between Vijayanagar, Rajputana and Bihar (or something similar). At this point, make sure you're not allied with Vija and strike whenever your overlord is convincingly beaten (no army, 12+ WE, no allies, only a few provinces not occupied) by the other two nations. Siege a few provinces at a time while keeping a mobile army that sits on top of whichever enemy province will next finish building a unit and it should be doable with honest means.
Really, being a vassal isn't particularly bad for a minor as it offers a nice measure of security so don't rush to independence. While you remain non-sovereign, you may as well disband your starting army as you won't need it for anything, it just costs money. Don't bother rebuilding it until you have at least all tier-1 buildings up and a healthy economy running. Ships are different, they cost next to nothing to maintain but are much costlier and slower to build than armies. Cost reductions for ships also come only with the tier-3 building, while armies gets cheaper with the tier-one armory. Keep the starting fleet, disband the army.
Of course, there are gamey tricks that let's you beat Vija much earlier if you know them. The easiest exploit is that an AI army will not start moving if a smaller/weaker stack is marching towards it. By having a force do this perpetually (pause, cancel move before it completes, restart move, unpause) you can keep a doomstack in place with a single regiment - leaving the rest of your forces a relatively free hand. Takes tons of patience though as you probably need to cancel/restart the move lots of times during a single war.
I only use it truly bad situations though, like Kashmir vs. Timurids, Lorraine vs France+Burgundy or Navarra vs Castille (in all cases, I hadn't expanded prior to their attacks). It just isn't worth the time, concentration and effort for something where annexation isn't otherwise inevitable.