Have the client create a YouTube channel and create playlist(s) within that channel. Then the client can just tell you which playlist(s) to include on the site and you can pull in all the videos within specific playlists via the YouTube API.
This way you set it (once) and forget it. And the client can maintain the playlists within YouTube as they see fit and know that the videos within those playlists will be automatically included on the web site.
Here are some sample code snippets:
// Init service.
YouTubeService service = new YouTubeService("MyApplicationName", "MyDeveloperApiKey");
// Get playlists for youtube user (your client).
PlaylistsFeed playlists = service.GetPlaylists(new YouTubeQuery("http://gdata.youtube.com/feeds/api/users/[CLIENT_USER]/playlists"));
// Get playlist feed.
PlaylistFeed feed = service.GetPlaylist(new YouTubeQuery("http://gdata.youtube.com/feeds/api/playlists/" + playlistID)));
// Get list of video IDs for playlist.
(from atomEntry in feed.Entries select (atomEntry as PlaylistEntry).VideoId).ToList());