"Nappy" meaning diaper is an unknown usage in the US.

In its non-racial sense, "nappy" means having a "nap" or fuzzy surface like a carpet.

Here are some examples found on the Internet:

"Suede: Abraded leather with a nappy surface"
(from a "glossary of shoe and handbag terms")

"Shetland: A soft, light, tweed-like, very nappy fabric...
Tweed: A rough, wiry wool with hairy, nappy surface..."
(from a glossary of men's clothing fabrics)

These days it's hard to find an instance of the term "nappy-headed" that was NOT inspired by Don Imus, but I found a few:

At Women Make Movies:

Hair Piece: A Film for Nappy-Headed People
A film by Ayoka Chenzira
1985, 10 minutes, Color, VHS/16mm
Order No. W99218

An animated satire on the question of self-image for African American women living in a society where beautiful hair is viewed as hair that blows in the wind and lets you be free. Lively tunes and witty narration accompany a quick-paced inventory of relaxers, gels and curlers. Such rituals are all-too familiar to African American women-and indeed to all women confronted with an unattainable ideal of beauty. This short film has become essential for discussions of racism, African American cinema, and empowerment. Used by hundreds of groups as diverse as museums, churches, hospitals, and hair stylists.

At Author's Den this paragraph introduces a poem called "Nappy Headed" by Latasha A Willis:

I wrote this poem on February 20, 2005. At the time, I was frustrated about how kinky/coily/nappy hair is still frowned upon by many in the black community, especially for black women. I stopped relaxing [i.e. straightening] my hair in 2002, and I enjoy my natural hair texture. The poem is meant to encourage other black women who went natural or want to go natural and are afraid of how their family and peers will react if they ever went through with it.