Ask Mr. Smarty Plants

I  have not been able to find a source for fruitless olives in your vicinity.  What you have may indeed be Cordia boissieri, but it could also be a totally different olive species, such as Swan Hill Olive ®, grown on the Olea europaea cv, "Oblonga" rootstock.  This latter tree is the most popular of several related fruitless olive species.  Other cultivars are Wilsonii and Majestic Beauty.  Texas nurserymen are very enterprising, and I suspect that if these fruitless olives were well suited for Texas they would be more widely available.  Their absence is likely due to their cold sensitivity.  C. boissieri is said to survive only down to 20 degrees F., and O. europaea will be lost at 28-26 degrees F.  Your tree must be in a well protected spot, or you have just been lucky with the weather.

I am not very familiar with these non-native trees since our specialty is native plants.  You can find more information at nursery sites in Arizona and California.  You can probably mail-order trees from there.  However, I think it would be risky to try and grow these species.  Over the next few years we are likely to have at least one really cold spell that could take them out.

You might want to consider planting a cold-hardy native tree that has a growth habit similar to the olives.  I could suggest Ebenopsis ebano (Texas ebony), Diospyros texana (Texas persimmon), Sophora secundiflora (Texas mountain laurel), or Ilex vomitoria (Yaupon).  If you visit the Lady Bird Johnson Wildflower Center web site of plant suppliers and enter your zip code or address you will find names of local native plant suppliers.

Shown below are images of the native trees that I recommend.