...will charge via AC adapter. It's usually a given that they charge via AC adapter, which is probably why you couldn't find anything in your search results. The ones that don't usually take regular alkaline or rechargeable AA or AAA batteries. I think those are getting scarce.
Anyway, you just have to find an adapter. Most players don't come with one. It's usually an optional accessory. You can either buy an adapter from the maker of the player (look at the manufacturer's website to see if one is available) or you can buy a universal adapter. I have a universal adapter that I bought from WalMart (it's called musicPower Duet) that can charge two players at once. It has 2 usb-like ports to plug your player(s) into and then you plug it into your wall outlet.
You haven't included any more specifics, so I'll just throw a few out there and you can see if any of these interest you. Since you're not interested in higher capacities, I'll leave the hard drive players out.
From SanDisk: Sansa Express, Clip, e200 Series
From Creative: Zen Stone Plus, Zen, Zen V and V Plus
From Apple: iPod Shuffle, iPod Nano
You can also look at CNET's mp3 player page:
I've decided that I NEED an MP3 to survive my lone-train rides.
Alas there are a few things I "demand" from my MP3 but no site I have found has shown me a way to filter, hench I ask for your help
I want an MP3 that will:
-Have 1-2 GB of space (I don't need really more)
-Will be able to recharge through a direct connection to AC (or some kind of adapter) In other words, I will not have a computer for most of the time and I'll have to use the normal power supply to recharge the chosen MP