Why don't Transport Category aircraft have a listed Vy?
Large commercial jets operate within a much wider range of weights than most GA aircraft do, and since Vy varies with weight, it wouldn't make sense to publish "a" single Vy speed for them. The crew can get a best rate or best angle of climb speed from the FMC (which "knows" the current weight of the aircraft, based on current fuel &amp; an entered Zero Fuel Weight). 

From an empty aircraft with minimum fuel to a loaded aircraft with max fuel, the weight probably won't quite double for most commercial jet aircraft, but the one might be 170% or more of the other. With that much range, any single Vy you publish would be way far off in a lot of cases. On a GA aircraft, without an FMC and operating in a much narrower weight range, publishing a single speed makes much more sense as the delta between published and actual becomes smaller and the consequence of being a couple knots off is probably slight.