I loved my Mimosa's when we were in Hawaii. They were called "Monkey Pod Trees" there. I still am homesick for them, despite all the negatives about them. Sitting underneath one, in dappled shade, and watching the clouds in a blue sky slide by just past the lacy canopy of the Mimosa leaves was well worth all of it to me (and obviously to many other Hawaiian residents as we all had em.
I cannot grow them here (and have never heard of a seedless one) so had to find SOMETHING like it that would survive in my new home in eastern Washington. I discovered the THORNLESS Honey Locust (which differs IMMENSELY from the really nasty regular Honey Locust Tree in that it has no flowers, so no pods, and no thorns - only leaves - and never drops anything but it's leaves once a year in the fall ... when the winds are high and they simply blow away on the wind as they are smaller than my little fingernail.) This tree has leaves on shafts that look lacy in almost exactly the same way as the Mimosa, but there is no canopy effect. They do branch out sideways, however, far enough to make a small canopy if you trim the branches up to an area over your head before allowing the tree to set branches.
This one might work for you. It's in DavesGarden at http://davesgarden.com/guides/pf/go/74376 though it is there with notations and photos about seed pods and flowers. Honestly, they are growing all over up here and I've never seen a flower or a seed pod, or any thorns, so wonder if someone didn't mix the information on the general Honey Locust (which has some really viscious, nasty thorns) into the THORNLESS Honey Locust info sheet area...?????