It seems that you cannot put your desired default options in a config file.
If you know about $PATH you can resort to a hack.
Create this script:
#!/bin/sh
feh --bg-color black "$@"
Call it feh and place it in your $PATH before /usr/bin/ (assuming that feh itself is in /usr/bin/).
Some distros have ~/bin/ in $PATH by default. So you would put that script into ~/bin/ (and make it executable). Otherwise just create this folder yourself and prepend it to your $PATH.
Also, if you want to set multiple default options, you can group them into themes. (Theme is the feh developer's name for a named group of options.) Create ~/.config/feh/themes and add this line to that file:
default --bg-color black
feh -Tdefault will then start feh with your desired default options. This is handy if you want to set multiple options at once. Unfortunately there is no way to set a default theme either. So, in your case it doesn't help. But you can fallback to the same hack as above:
#!/bin/sh
feh -Tdefault "$@"
Alternative:
If you are just going to call feh manually from the commandline, you can instead set an alias in your shell. In bash you would add this line to your ~/.bashrc and restart the interpreter (e.g. re-open the terminal):
alias feh="feh --bg-color black"
In fish shell you would run:
abbr -a feh feh --bg-color black