We have been using Nextcard credit cards which gave us gift
certificates redeemable at Amazon The more we use the card the more we
could redeem. As of July 10 Nextcard credit card company is no longer
in business. We got used to having the Amazon credit. Is there another
credit card company that offers Amazon credit instead of miles? I
contacted Amazon and they said that They are not affiliated with any.

visa.yahoo.com

1% of your orders will be translated into Yahoo! Points. You can
exchange the Yahoo! Points into SuperCertificates with
GiftCertificates.com. You can then redeem the SuperCertificate for an
Amazon gift certificate.

For example, $2,500 spent -> 2500 Yahoo! Points -> $25
GiftCertificate.com's SuperCertificate -> $25 Amazon.com gift
certificate

This link has a great overview of cards and benefits:
http://www.expertcredit.com/expertcredit/first-usa/vendorid_9-wide_0/vendor.htm

In addition to the Yahoo card mentioned above, you may also be
interested in the Borders card that you will see listed on the site
above.
$20 Borders gift card after first purchase 
$1 spent at Borders = 2 reward points earned 
$1 spent elsewhere = 1 reward point earned 
Receive a $5 certificate each time you accumulate 500 points 


Apparently, Borders has "teamed with Amazon" and Amazon rewards points
for "Borders" orders provided they are not shipped to international
addresses.  You can read about it here:
http://www.amazon.com/exec/obidos/tg/browse/-/518224/

It might mean you have to order from borders.com, but, that appears to
be amazon.com.  You might want to double-check with Amazon and the
credit card company just to be safe... I don't use the card, so I am
unable to confirm.