There was a partnership between FIRST and Girl Scouts announced in 2008 or 2009. Two years ago, they offered the patch shown in the link below. Girls could earn it by participating in a qualifying event ( for us, the regional tournaments). I ordered the patch for my daughter, I think from the national GS website.
It does not seem to be available in the GS shop anymore, so I don't know the status of the partnership.
I think that FIRST would be open to GS tables. I would start with contacting the individual tournament organizers.