An old Irish drinking song:
“Water is Alright in Tay”
It’s not literally wine, but:
“Brown eyed women and red grenadine\ The bottle was dusty but the liquor was clean.”
Red Grenadine, The Grateful Dead
Summer Wine, Nancy Sinatra
Aww. I went and found two songs about cocoa too.
Supergrass have a whole album called ‘I Should Coco,’ an intentional mis-spelling of cocoa (“I should cocoa” = “I should say so” in Cockney rhyming slang; you’ll still hear it said even nowadays).
And the Von Trapp Children apparently sang A Hot Cup of Cocoa, as did some elementary schools around Christmas.
You don’t need them now that you’ve made the sensible decision to switch to hot chocolate, but I found them so I’m going to post them anyway.
Apparently some folks do:
Lips as sweet as candy.
Their taste stays on my mind.
Girl, you keep me thirsty for another cup of wine.
(“Hooked on a Feeling” - Mark James)
Here are a few more I thought of:
Joni MItchell - “Carey” (Come on down to the Mermaid Cafe and I will buy you a bottle of wine…)
XTC - “We’re All Light” (…and I’ll leave nothing here but love and milk a’ plenty for your tea…)
Paul McCartney - “Cafe on the Left Bank” (Cafe on the left bank, ordinary wine…)
Steve Goodman - “The Dutchman” (Some tea with whiskey keeps away the dew)
Isn’t there a Paul McCartney Beatles song with a phrase like “went downstairs & poured myself a cup”? I remember him snarking about a magazine ad for coffee that used it.
A Day In The Life, The Beatles.
Relevant lyrics:
Ah, that sounds like it.
Otoh, the paper cup in “Across the Universe” doesn’t seem to have a beverage in it.
You don’t drink mulled wine in a cup? 
Or, oh my gosh, burned rhum? Them things are hot, hot, hot, you want a handle to be able to handle them! Plus, in some parts of the English-speaking world, cups have stems, not handles. Matter of fact, it’s the term I was taught in ESL class for “a glass with a stem”. I would say that the Stanley Cup resembles an ice-cream cup more than it resembles a teacup, handles notwithstanding…
Oh, and I imagine they won’t be acceptable, but I like both Bosé’s “Café” (he’s a very, very, very bad boy and can make “you give me coffee” sound like a whole encyclopedia’s worth of innuendo) and 440’s “Ojalá que llueva café en el campo” (“may it rain coffee on the fields”).
Tea Mania: Elemental - Cup of Brown Joy: “If you’re tired of tea, then you’re tired of life”, and many more.
Well, if we’re doing Paul McCartney, there’s “Uncle Albert/Admiral Halsey.”
Lyrics:
Admiral Halsey notified me
He had to have a berth or he couldn’t get to sea
I had another look and I had a cup of tea and a butter pie
(“A butter pie?” “The butter wouldn’t melt, so I put it in the pie”)
How about the group “Hot Chocolate” - Emma, Everyone’s a Winner, You Sexy Thing - ?
And I almost forgot…
Jermaine Stewart “We Don’t have to Take Our Clothes Off”
…We could dance and party, all night
and drink some cherry Wine…uh huh…
U2, Achtung Baby, The End of the World:
We ate the food
We drank the wine
Everybody had a good time
Except you
Sarah McLachlan, Fumbling Towards Ecstasy, Ice Cream:
Your love is better than chocolate
Better than anything else that I’ve tried
Sheryl Crow, Everyday Is A Winding Road [sic!]
I’ve been swimming in a sea of anarchy
I’ve been living on coffee and nicotine
The Nutcracker has songs dedicated to coffee, tea, and chocolate, right? No lyrics tho.
My Coco, by Stellastarr
http://www.metacafe.com/watch/sy-5749502/stellastarr_my_coco_official_music_video/
There’s a song by Dada called “The Ballad of Earl Gray and Chamomile.”
Kristin Chenoweth’s Taylor, The Latte Boy.
How about chocolate milk? It’s just cold cocoa, right? Rufus Wainwright wrote Cigarettes and Chocolate Milk.
Coffee:
Take Me Out To Eat - on the album Buy Me Bring Me Take Me: Don’t Mess My Hair - Life According To Four Bitchin’ Babes, Volume 2
Butter - on the album Buy Me Bring Me Take Me: Don’t Mess My Hair - Life According To Four Bitchin’ Babes, Volume 2
Wine:
The pub with no beer - There are many that play this.