Hello djmercury1.
I understand your Photosmart 6510 is indicating that the "Photo Tray Is not installed". I would like to verify something: Have you always selected "photo tray" when trying to print a photo?
Usually you will have this feature available when you have a "photo tray" installed on your printer. You only have one paper tray installed on your printer. This is probably why you have a yellow sign next to photo tray.
You can try taking out your paper tray and pushing it back into the printer to see if this makes a difference.
I would suggest changing the settings within the program you are printing from. Please follow this HP document on Print Photos Saved on Your Windows Computer. If you don't have a Windows computer, please let me know. Try changing the setting to tray one instead of photo tray.
If you have any further questions, please let me know.