How to colorize a black-transparent PNG icon with ImageMagick

You can use one of the following commands:

$ convert input.png +level-colors "red", output.png
$ convert input.png +level-colors "rgb(255,0,0)", output.png
$ convert input.png +level-colors "#ff0000", output.png

Note that the , character is important here. On the left side of the , character we tell convert which color should replace black and on right side what color should replace white. Therefore nothing should be given after the , character.

Source

... how do I colorize black & transparent PNG images [...] to colorize them like this [...] using ImageMagick

The -fill <COLOR> option works fantastic for this purpose. You can replace "#1bbfc9" with a human-readable name (e.g. "red") or an HTML color code.

convert target-black.png -fill "#1bbfc9" -colorize 100 target-blue.png

... allowing to script and process hundreds of icons at a time

Using the find command, you can recurse hundreds.
Warning: This will replace the originals.

find path/to/files  -iname '*.png' -exec convert "{}" -fill "#1bbfc9" -colorize 100 "{}" \;