By default, the Session editor will include all of your uploaded custom fonts. You can use the "custom_fonts" parameter to specify the exact fonts you only want to be listed.
{
"template" : "TEMPLATE_ID_HERE",
"custom_fonts": ["bb_custom_font_1_otf", "bb_custom_font_2_otf"]
}
Ensure that you are using the classname that Bannerbear assigns to your uploaded fonts. You can get the classname when you poll a GET request to the /fonts endpoint or from the Custom Fonts page.
You can check the API Documentation↗ for additional info.