Using the built-in ObjectDataSource mapping up a separate datasource for each item is probably the only straightforward way (and the only way that's easy enough to be worth the effort...).
Is it a requirement that you use the ObjectDataSource, or can you choose a different way to get the data from the storage? I would recommend either using Entity Framework (which imho rocks) or creating your own custom types to which you get the data with a custom designed DAL (which is a lot more work than using EF, but if you're, like some, concerned that EF is still in infancy this might be your option).
In either case, you'll end up with a C# class called Program, which has properties of type IEnumerable<Stakeholder> and IEnumerable<Outcome> called Stakeholders and Outcomes respectively. You can then use these as datasources for the item repeaters and set them in the ItemDataBound event of the ProgramRepeater, maybe something like this:
protected void ProgramRepeater_ItemDataBound(object sender, ItemDataBoundEvent e) {
Program dataItem = (Program)e.DataItem;
Repeater stakeholderRptr = (Repeater)e.Item.FindControl("ProgramRepeater");
Repeater outecomeRptr = (Repeater)e.Item.FindControl("OutcomeRepeater");
stakeholderRptr.DataSource = dataItem.Stakeholders;
stakeholderRptr.DataBind();
outecomeRptr.DataSource = dataItem.Outcomes;
outecomeRptr.DataBind();
}
This is assuming that you're using ASP.Net WebForms, of course. In ASP.Net MVC it is even easier - you just send the Program object to the View as the Model object, and loop through its Stakeholders and Outcomes in a couple of nested for loops directly on the View.
Note: All code is provided as is, and I do not guarantee that it will run as expected or even compile. It is just to give you an idea of what to make your code do - not necessarily the exact code you need to solve your problem.