I’d like to put up a “No Soliciting” sign over my doorbell - the front face of my house is made from bricks like this one.
How can/should I do it?
Since it’s such a small/lightweight item, is there a way to do it without drilling?
Liquid nails.
If you must mount it on the brick (instead of double-sided tape to the door or something like that), just drill into the mortar, not the brick. Mortar is trivially easy to patch afterwards. You can either use small concrete screws or even ordinary screws with or without anchors. I’ve mounted lots of stuff that way, and it’s generally how cable companies fasten their cable clips.
3M or Gorilla make a very sticky two-sided mounting tape that will probably do it. From my experience with it put it on when it’s warm outside, not cold.
Mount it to your doorbell?
Another option is to replace your doorbell plate/button with one that includes a “no solicitors” statement.
Also, IME the “no solicitors” will have zero effect on the number of solicitors who will ring your doorbell. They all think you’re talking to some other solicitor.
Home Depot carries some pretty strong double sided “tape”. I used it to attach signs to the brick columns at our apt pool. 4 years and still holding on. The trick is to clean the bricks thoroughly first.