I'm looking for canon (both A Song of Ice and Fire and Game of Thrones) examples of genuine friendship between Cersei and another character. I am not talking about the love/lust she feels for Jaime or the motherly love she showed toward her children. I also am not talking about the lackie/servant dynamic with her most frequent hangout buddies Qyburn and Sir Gregor. Are there examples of friendship at any point in her life?
There is at least one character who Cersei considers to be her friend: Lady Taena Merryweather.
"Lord Merryweather and I wish only to serve Your Grace and the little king," the woman purred, with a look that was as pregnant as Lady Graceford.
This one is ambitious, and her lord is proud but poor. "We must speak again, my lady. Taena, is it? You are most kind. I know that we shall be great friends."
"I am growing very fond of Lady Taena. She amuses me."
"My queen?" said Taena Merryweather. "You have a strange look in your eyes. Are you unwell?"
"I was just . . . remembering." Her throat was dry. "You are a good friend, Taena. I have not had a true friend in . . ."
Well, he has a strong wife. It was a pity Taena could not serve as Hand. She was thrice the man her husband was, and far more amusing.
Throughout A Feast for Crows Taena serves as Cersei's close ally, confidant, and even informant. Cersei considers her to be the only person she can truly trust and rely upon. This is particularly remarkable given that Cersei knows that Taena is spying on her for Lady Margery Tyrell--a situation that Cersei not only allows to continue, but tries to twist to her advantage:
"If you know she is a spy, why take her on?"
"Margaery is not half so clever as she thinks. She has no notion what a sweet serpent she has in that Myrish slut. I use Taena to feed the little queen what I want her to know. Some of it is even true." Cersei's eyes were bright with mischief. "And Taena tells me everything Maid Margaery is doing."
At one point Cersei even makes sexual advances upon her, but despite Taena's apparent willingness to "serve her Queen" this aspect of their relationship is limited to a single night.
It was still no good.
It had never been any good with anyone but Jaime.
When she tried to take her hand away, Taena caught it and kissed her fingers. "Sweet queen, how shall I pleasure you?"
Personally I believe their "friendship" was very one-sided, with Taena in fact expertly manipulating her way into Cersei's good graces. We have no idea how she really feels about her Queen, considering how abysmal a judge of character Cersei proves herself to be. Taena has yet to reappear in the books following her flight from King's Landing during Cersei's imprisonment by the Faith.
She had friends, at least at one time.
Cersei and her friends Jeyne Farman and Melara Hetherspoon went to her during the tourney for King Aerys II's visit to the Westerlands, at which Cersei became enamoured of Prince Rhaegar Targaryen.