Not true about the white soles. Both of my kids are competitive tennis players, and none of their shoes have ever had white soles (see
http://www.tennis-warehouse.com/Junior_Tennis_Shoes/catpage-JSHOEMAKER.html for examples). Non-marking soles, yes.
Shop on one of the tennis websites (tenniswarehouse (my favorite), tennisexpress, midwestsports). Most of them have excellent customer service and free shipping, and roughly the same prices as zappos, which doesn't have many kids' shoes that are actually designed for tennis.