The hightly customizable plugin xili-postinpost is able since version 0.9.2 to display the result of the query according time or date.
Below one attachment appear in the morning and another appear in the afternoon
this is morning
The date kept is the date of the server that is set in General Settings of WP dashboard. Two shortcodes are present in content of the post and the query is here for the afternoon image: query=’attachment_id=1876′ to demonstrate that xili-postinpost use current WP loop syntax.
More infos here how to configure shortcodes !