Disclaimer: I do not own Doctor Who
There were times, after Amy and Rory had left, when River would go off on her own. Have some adventures by herself. Possibly meet up with a future or past Doctor. She always felt a little bad about leaving her Doctor alone, but she just had to get away. It wasn't that the Doctor was being depressed all the time, no it was worse. He would put on a happy façade and they would go off on adventures. No one else could see through the façade but River could.
There would be times when River would come down into the console room, or return from one of her own adventures and take one look at her Doctor and know that they wouldn't be going on any adventures that day. Instead, they would sit in the TARDIS and hold hands. Silently comforting each other.