puddles in my concrete patio
Self-leveling materials are usually not intended to be finished-surface products--they cure out to something rather chalky. You'd need to overlay something more durable. I suggest finding a self-leveling product that meets your needs, then overlaying quarry tile or porcelain. 

If that sounds overwhelming (it's not that difficult, just time consuming), You might just have to cut out the faulty portion and have it re-poured. You may find a deal by piggybacking on someone else's project. You might get lucky and avoid trip charges, or you could split them. Concrete isn't terribly expensive--it's the workmanship you pay for.