You are in luck here.
the EventAggregation in Prism isn't a function of the Unity container, but something that Prism automatically puts in the container for client classes to use. So classes declare they have an IEventAggregator dependency and an instance of that is given to that class via dependency injection. The thing to take away here: it's standalone.
So, you have several options.
If you don't need any of the other features of Prism (component modularity, etc) you can simply use Ninject and insert an instance of the EventAggregator into your Ninject container for the rest of your application to use.
If you want the other features of Prism, you can replace the DI container implementation. I wasn't able to find a specific example of this, unfortunately, but I think all you'd have to do was reimplement the base "UnityBootstrapper" type with one of your own making "NinjectBootstrapper". I think that UnityBootrapper is the only point at which the Prism components (EventAggregator, RegionManager, etc) come into contact with Unity (specifically in the implementation of "ConfigureContainer").
Edit: I'm wrong here. You also have to implement IServiceLocator with a Ninject-specific implementation. No big deal, though.
Embrace Unity. It's a pretty good DI container with a lot of flexibility. It doesn't have the fluent interface that Ninject does, but it's certainly not hard to use.
You can use another similar eventing system that is included in the MVVMFoundation (http://mvvmfoundation.codeplex.com). It's called the Messenger and it does pretty much what the EventAggregator does in Prism, but the library you download is much lighter.
Hope this is enough options for ya!