..the clamp diodes are missing...

I think is easy with L293D (internal clamp diodes)...if you combine the channels you have Peak Output Current=1.2A (check the specs of the solenoid)

If you need more current use TLE 5205-2 (peak=6A)

Both of the items should be at mouser.com

...please check also this tutorial to understand better the h-bridge circuit http://www.robotroom.com/HBridge.html