Hi,
As I understand, you encountered the error when you create a new page using the custom page layout in the sub site in SharePoint 2010.
You could check if the data view is in the page layout.
If the data view exits in the custom page layout, you could follow the trouble shooting steps:
1. Check if you have the permission in the list inserted in the page layout. You could go to the list to check the user permission of the account. If you do not have the permission in the list, you could add the permission in the list for the
user.
2. You also could edit the OwssvrHandler feature permission for the site, then do IISReset. For more detailed information, you could refer to the article below.
The article below is about List does not exist. The page you selected contains a list that does not exist. It may have been deleted by another user SharePoint 2010 error.
https://shareyourpoint.wordpress.com/2012/04/12/list-does-not-exist-the-page-you-selected-contains-a-list-that-does-not-exist-it-may-have-been-deleted-by-another-user-sharepoint-2010-error/
3. Check if it can work if you remove the data view in the custom page layout.
More reference:
https://social.msdn.microsoft.com/Forums/office/en-US/150aca88-c32c-4dbf-9f79-638ae438d1a0/systemruntimeinteropservicescomexception-list-does-not-exist?forum=sharepointgeneralprevious
Best regards,
Sara Fan