Hi! Activated charcoal is used for when beardies eat something toxic; not so much for constipation, though the water in the solution might help a little.
There are several things you can try to get them moving. You can try
bathing them in shallow water because that sometimes gets them in the mood to go. You can also feed them certain organic baby foods and try dripping water on their snouts if they're a little dehydrated so that they drink. Also, diet, UV lighting and temperatures are very important. Things like dry mealworms and superworms can get them stopped up, as can improper husbandry around UV and temps, which need to be within a narrow range to help them properly digest and metabolize nutrients.
If you can post details on these items, we can better evaluate the situation & advise.