You could create Factory beans and inject that into your A class, then call a method on it to create the B.
Just a thought of the top of my head, sorry I didn't think too hard on it for too long.
The main point with Spring and dependency injection is for you not to call "new"
there are beans that you can create and in the configuration set a factory-method or an init-method that it will call.
Look at the FactoryBean interface too to see if that might help.
If not, and you come across a situation that can't be resolved, look closely at the design there is usually a problem there that causes the tough situation. That is my motto.
Mark