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Billy owns an antique baby grand piano manufactured by J. Bauer & Co. in the 1920s. He bought it in Chicago in 1993 around the same time he bought his new house (the one he's living in at the moment, the Victorian style thing). "The piano luxuriates in front of a window" (pictured).
 

From the Jim Stapleton book:

Looking forward to what the band could accomplish in the New Year, Billy and his wife saw 1993 out hosting a small party at their new home. The guests included BIlly's friend Jimmy, who played in a radical art group from Milwaukee called The Frogs, Corgan's favourite band. They kept the party going by playing appalling tunes from the Seventies on the Corgan's grand piano. Jimmy managed to answer every request that was thrown at him: from Badfinger's "Baby Blue" and Elton John's "Rocket Man" to THe Raspberries' "Go All The Way". As the night wore on, everyone began to recognize that Jimmy knew every awful Seventies' song imaginable. Billy saw the New Year in, rolling around on the floor, doubled up in uncontrollable laughter.
 

The piano pictured here is very similair to Billy's in that it is a 1920s J. Bauer & Co. baby grand piano. Wow. : )

 
I found this in an interview transcript:

Between endless touring and recording, he's returned to his century-old home in Chicago, where ancient wood beams lace the living room ceiling, built-in wood cabinets line the walls and an intricately molded fireplace adorns the dining room. A long window of curved glass sheds opaque light across a baby grand piano, the one Corgan used to kick off the Pumpkins' most recent album, Mellon Collie and the Infinite Sadness, and gives the rest of the room's antique furniture a warm glow. A framed snapshot of Corgan and his wife, Chris Fabian, during their ong-haired-rocker phase, is displayed on a hall bureau amid a collection of prewar photos, while the couple's two black cats, Thelonious and Lily, play on flowery throw rugs. Even the steam heaters in this five-bedroom house are beautifully ornate.
 

And what about James and D'Arcy? Well, James himself owns a grand piano, which was used alot on his album "Let It Come Down." His piano resides in his living room on the first floor of his house.

We can pretty much assume that D'Arcy would have a piano in her house somewhere (especially since she's got a home studio..).