You could use the AvailableContentTypes attibute on your ContentModel classes to define which models that should be availble under that model, like following from Alloy:

 [AvailableContentTypes(
        Availability.Specific,
        Include = new[] { typeof(ContainerPage), typeof(ProductPage), typeof(StandardPage), typeof(ISearchPage), typeof(LandingPage), typeof(ContentFolder) }, // Pages we can create under the start page...
        ExcludeOn = new[] { typeof(ContainerPage), typeof(ProductPage), typeof(StandardPage), typeof(ISearchPage), typeof(LandingPage) })] // ...and underneath those we can't create additional start pages
    public class StartPage : SitePageData

How does the definition of the content type that is unable to be created below startpage look like?

Thanks for the responses, Henrik the type that isnt allowed is an inbuilt system type.

    //
    // Summary:
    //     /// Represents a folder in a content tree. A content folder is used to structure
    //     content and has no visual appearance on the site. ///
    [AdministrationSettings(GroupName = "systemtypes", Visible = true, CodeOnly = true, Order = 10000)]
    [DebuggerDisplay("{DebuggerDisplay,nq}")]
    public class ContentFolder : BasicContent, IReadOnly<ContentFolder>, IReadOnly, IContentSecurable, ISecurable, IRoutable
    {


}

Thanks Johan we'll try explicitly adding the system type page as allowed. 

We have also found that in Epi Admim under "StartPage", we've just set allow all on content types and this seems to resolve it, however this approach feels more like a work around.