“Old Red Wine” by the Who
“Have a Cuppa Tea” or “Afternoon Tea,” both by The Kinks.
Blind Melon’s “No Rain”
*All I can say is that my life is pretty plain
I like watchin’ the puddles gather rain
And all I can do is just pour some tea for two
and speak my point of view
But it’s not sane, It’s not sane *
“Will You”, Hazel O’Connor.
You drink your coffee and I sip my tea
And we’re sitting here playing so cool,
Thinking “What will be, will be”
The Coffee Song–by The Chairman Of The Board, Old Blue Eyes, Frank Sinatra!
My favorite: “Coffee in a Cardboard Cup.”
If champagne is being counted, then don’t forget Queen’s “Killer Queen” (which mentions Moet & Chandon in the opening lines).
As far as regular ol’ wine, let me also mention the Replacements’ “Red Red Wine” (a totally different song than the Neil Diamond one). It ticks off several varieties in the lyrics, including Chateau Timberlay, Gallo and muscatel. Also, it rocks pretty hard.
And if you want a crappy fortified wine – like for a lower-ranked card – Guns ‘N’ Roses did “Nightrain.” But there may not be a lot of associated recipes.
From You Don’t Love Me Anymore (Al Yankovic)
Does it have to be wine or can it just be alcohol? Because if it’s the second, you may want to take a trip to the Country Songs aisle of your local music provider, or hie thee to the Scotts’n’Irish Traditionals.
Whiskey in the jar
Tequila - although it’s a bit short on lyrics 
Tequila sunrise - Eagles
It’s five o’clock somewhere - I’m not sure which specific beverages get mentioned, can’t go to “entertainment” websites at work
The most fitting hot chocolate song is “Hot Chocolate” by Shonen Knife.
Another tea one - “Tea for One” by Kevin Gilbert.
The Cardigans “I Need Some Fine Wine”
Tricky & Bjork “Black Coffee”
Some oldies but goodies:
You’re the cream in my coffee, you’re the salt in my stew…
Just around the corner,
there’s a rainbow in the sky,
So let’s have another cup of coffee,
and let’s have another piece of pie.
And while there are a lot of songs called Black Coffee I rather like this one from 1935 (not the later one made famous by Sarah Vaughan, which is also excellent).
The Weavers’ “Kisses Sweeter Than Wine”
Led Zeppelin’s “Tea for One”
Cocoa is going to be tough. You can’t do whiskey instead?
Cheap Wine (and a three day growth) Cold Chisel
Or beer?
Who drinks wine in a cup?
We decided the 69th card has to be wine (since 1969), so that makes it pentacles. Coffee is cups, tea is swords and cocoa is wands.
Okay, we’rd going with chocolate songs instead of cocoa.
Tom Paxton also wrote songs mentioning tea (About the Children) and coffee (Victoria Dines Alone). One wine song that hasn’t been mentioned is “Sweet Cherry Wine.”
ETA: Thanks again. This is getting interesting.
The Beatles’ “Lovely Rita”: “May I inquire discreetly/When are you free to take some tea with me…”
The Rolling Stones’ “Live With Me”: “I got nasty habits/I take tea at three…”
‘Coffee and TV’ - Blur
“Sweet Like Chocolate” by Shanks & Bigfoot
“What’s the Use of Getting Sober (When You’re Gonna Get Drunk Again)” - Louis Jordan (later covered by Joe Jackson):
Leonard Cohen’s “Suzanne” feeds you tea and oranges that come all the way from China.