Interesting fact about the Repeater solution is that you can use it to build any kind of generic asp.net control that will be perfectly specifiable in mark-up.
I am writing a GenericeControlBuilder that will not be specific to the single control type, but I didn’t have enough time to finish it yet.

The interesting question is how to implement fully generic TemplateContainerAttribute. Dynamic creation of the attribute is not a problem at all — solved in the article.
But the question is how to know right TemplateContainer type in a GenericControlBuilder that has no hardcoded information about the control it creates.
I consider adding another attribute that will specify how control type arguments map to the TemplateContainer type arguments.

public class Repeater {
    …

    [GenericTemplateContainer(typeof(RepeaterItem<>), UseParentTypeArguments=true)]
    public ITemplate ItemTemplate

    …
}

This is just to show the basic idea — this syntax is way too limiting.