I have Fireworks somewhere, but I can't find it. I prefer Fireworks, too. In fact, I made all three of my emoticon DDs with Fireworks. The first two were with the vector tools (I know, vector tools for regular sized emoticons? ), and my latest DD was solely with the pencil tool.
Try GIMP. It has a pixel tool (just size down to 1.) And you can animate with it in the program itself by exporting as a gif file! Here's the download: [link] I use it almost all the time, so I suggest you try it. It's free forever, and internet download meets your criteria, as you said.