This page has a super-nice chart and goes down into the wire sizes that I am using. It also does a good job of explaining the sources of the ratings and how conservative they are. It does seem to be specific for solid core wire though, which is a little inconvenient since my wiring is always stranded. http://www.powerstream.com/Wire_Size.htm
This page has a chart that addresses stranded wire. So far I haven't been able to find what source they are using though. It might be from the NEC. http://www.engineeringtoolbox.com/wire-gauges-d_419.html
Most of the tables that come up under Google Images are either for house wiring or concerned with a 3% drop round trip for DC 12V. Again, it doesn't seem as though these tables relate to stranded wire. Here are links to a few that might be about solid core wire or not:
http://edsboattips.com/wp-content/uploads/2013/03/voltage-drop-table.jpg
http://www.electric-skateboard.builders/uploads/db1493/original/2X/b/b041f15a19d7d5c9c0d478894688331a5e3d11e9.jpg
This one at least goes down to 1A: https://cdn.sparkfun.com/assets/f/d/2/3/3/51155039ce395f5e3d000002.jpg
Update 11/15/2018: Here are a few more links for when I was specifically trying to determine a current rating for 22 AWG stranded wire:
I am greatly amused that StackExchange has a section for Electrical Engineering, where I can find people asking dumb questions like mine without having to ask them myself. Here is "Can I pull 2 amps thrugh 22 AWG wire?" This person is also trying to figure out stranded wire, and not really getting an answer aside from an unsourced "it will be fine". But there are a few interesting links from this article. https://electronics.stackexchange.com/questions/350291/can-i-pull-2-amps-through-22-awg-stranded-wire
Here is an interesting table from Gore which seems to be derated for stranded conductors, but it's not explicitly stated: https://www.gore.com/IndustrialCableConfigurator/popup_hfr_wirespecs.html
This Wikipedia article addresses stranded wire by noting the differences with the calculations normally used for solid wire: https://en.wikipedia.org/wiki/American_wire_gauge