What Type of Phone am I Looking For?

[GGD]

There may be other similar models, but I found this Panasonic KX-TSC11B model that seems to meet your requirements.

No AC adapter, uses 3 AA batteries, manual says to change them every 6 months.

http://www.amazon.com/Panasonic-KX-TSC11...B0007Q3QSK
http://shop.panasonic.com/shop/model/KX-...?t=manuals&support#tabs

More looking, here's another one - AT-CL2909WH, 4 AA batteries.

http://www.amazon.com/AT-CL2909WH-Handse...B001S2PKPE

Looks like quite a few of these AT&T corded phones can work using just batteries.

http://telephones.att.com/telephones/cor...ingle-line