my dad is a ham so he always has antennas mounted on his cars
most of them he has drilled holes of some kind
on his pilot he got ones that mount to the roof rack, they work great, but on a civic unless you have a rack it wont be helpful at all

if you are handy and want a project i would look into buying a spare radio antenna plate, the one that goes above the drivers door on the roof
then try to attach the antenna to that and replace the stock radio antenna with your new cb antenna
im not sure how big your antenna is, but it seems like it may work, and it gives you a mounting surface that is replacable and also hides all wires since you can run it down with the old radio antenna

besides that idea i cant think of anything else that actually holds up very well, i have seen some that mount to glass and they seem decent, but usually the glue wears out after a while and it needs to be replaced

good luck though, maybe try posting in a ham forum and see what they have to say