Wikipedia lists it under its Latin name (Dalbergia sissoo), and says it's from the Punjab region. You might find it sold under a variety of names such as Shisham, sissoo, sisu, sheesham, tahli and Indian rosewood. Wikipedia says, "After teak, it is the most important cultivated timber tree of the Punjab - which is the largest producer of shisham timber in Pakistan and India, although it is the provincial tree of the Pakistani Punjab". Maybe there is a Pakistani or Punjabi furniture manufacturer in your area who can give you the name of a supplier.
And that's officially everything I know about sheesham. Hope you find it.