I have a backyard and I live off the Mediterranean Sea in the Middle East. I'd like to plant a tree today that would grow fast enough, be strong and stable and shady enough to allow my grandkids to build a tree house on top of it in a few years time. My backyard's garden currently consists mostly of olive trees, a pomegranate tree, a lemon tree and a few bushes.
It's not so much the variety of tree which counts for making a small treehouse, it's more its maturity, size, climbability, and particular forking of branches that make it a suitable subject for one. Most amateur treehouses are erected in trees that provide those conditions, and they will usually be 70-90 years old or more, with a trunk girth of more than 6 feet, more usually over 8 feet.
Olive trees are quite capable of becoming very large indeed over time in your climate, but given the time span you're talking about, it's probably not going to be possible to use one for a treehouse on its own. If you have many olive trees already, then constructing a more professional arrangement of platforms and roof which takes account of the trees' needs and doesn't put too much weight/stress on any particular tree is probably best. Having more than one olive tree (or any other tree) planted in an area is useful for this purpose; for ideas and some information, take a look at this article: Architect Sees Unique Challenge in Olive Treehouses. Although the arrangement shown in the photograph is probably much larger than you had in mind, this idea can be downsized or adapted with a bit of imagination, and depending on the tree planting which exists.