B&J Fabrics has Sunback lining for coats and jackets in loads of colors, even some prints, like this paisley above.
A relative of mine just bought a really cute duffle coat at J. Crew Factory, but after wearing it this weekend she realized it wasn't going to provide her much warmth. So I told her I'd replace it with a heavier lining fabric, known as Sunback or Kasha lining. It's satiny on one side and like a soft flannel on the other. Really boosts the warmth factor without adding bulk.
I called the fabric stores in the Garment District I thought might carry Sunback lining: Mood, Rosen & Chadick, NY Elegant and B&J. Mood only has it in hunter green ($12/yd), Rosen & Chadick carries only a couple of colors and charges $20/yard, and NY Elegant has several colors at $12.99/yard.
But B&J has oodles of colors, even a print or two, at $10.95 a yard! That's lower than the online prices I've found for Sunback lining. I never thought B&J would be the winner in this category, but there I go again, underestimating this store. I bought two yards of Sunback lining in a paisley print (photo above). Call them at 212-354-8150 and ask for swatches, or visit their web site: B&J Fabrics. Tell them Shop the Garment District sent you!
Note: I swear I saw Paulina Porizkova buying fabric in B&J when I was there. Had to be her.