There are a few options.
One is to use a nested Repeater to display the RadioButtons.
The other is to create the controls during the original repeaters. Repeater.ItemDataBound event.
In either case, you need to be very aware of the Page Lifecycle.
You'll want to avoid databinding in the Page_Load event, unless the databinding is being done with an if(!Page.IsPostback) block. If you fail to check for postback, you'll run into issues where the Page_Load calls a DataBind() call that then wipes the values of the repeater before any event handlers can use it.
Alternatively, you can do your binding in Page_Init, which occurs BEFORE the viewstate can be applied, so you won't lose your values.
You can also use USer Controls for the RadioButtons. There's a previous post that covers how to use nexsted user controls within a Repeater here.