I suspect I'm not the only one here who finds himself with a dormant math circle due to quarantine. I'm interested in two kinds of suggestions regarding this situation:
suggestions for running a math circle remotely, to the extent that the best practices are different from what one would do for a class, as recorded in How shall we teach math online? (e.g., how to recreate the participation-, exploration-, and activity-heavy nature of a math circle compared to a perhaps more typical math class); and
suggestions for good resources for math circle participants when the circle co-ordinators are not able to devote the resources to running an offline circle.
I'm in situation #2, but I assume that #1 is of interest, and the questions seem closely enough related to put them together. The circle of which I'm a part is for US 5–9 graders (roughly 10–14 years old); I'm open to suggestions at any level, but, if that makes it too unfocussed, then we can focus on that age range.
Question #1: This thought comes from teaching college classes, but may help a math circle too. You can communicate more often online, so you can keep them playing with ideas by sending out daily puzzles. Or you can send out a few puzzles related to your topic a day or two before "meeting", to get them thinking.
Question #2: For 5th to 9th graders, assuming not much facility with algebra, but some, and assuming they enjoy math.
Geometric construction (as mentioned in my comment): here (sciencevsmagic.net/geo) and here (euclidthegame.com). The two sites have some overlap but very different presentations and choices of challenges. Euclidthegame uses geogebra, so you can try your constructions there too; 25 levels. Sciencevsmagic does not; 10 shapes, 4 challenges for each. (Euclidthegame has comments, which sometimes contain helpful hints, sometimes contain wrong info, and sometimes are not suitable for kids.)
Modular arithmetic can be fun, and might make questions about Pythagorean triples accessible. You can look up Pythagorean triples, and you'll find lots of information. Or you could start with my blog post on it. Not modular but related: I ran a math circle for families in my home, where we used base 3. Here's my blog post about that.
Rodi Steinig does amazing math circles and has blogged extensively about them. Some will translate to online. Perhaps this voting one would be interesting?
At a technological level, teleconferencing systems like Zoom, Google Meet, etc. often have "virtual whiteboards" which can be shared by a group of participants in a meeting. If the participants have touch screens and preferably a stylus, they can write on the virtual whiteboard.
Access to touch screens and styluses is not as common as I'd wish, but you might be surprised by how many of your participants can do this with (e.g.) an iPad or a Google Chromebook.