The short answer
Many do. Most medina riads offer family suites or connecting rooms, and a typical family suite sleeps two adults and two children with a private bathroom. Some riads keep cots, extra bedding and a simple children's menu, and a few can be booked exclusively. Space is tighter than in a hotel, so check the layout first.
In more detail
Riads are small houses, so rooms vary a lot. Many offer a family suite, often with a double and two singles under one roof, or two rooms that connect. A family of four usually fits well. Bigger families either take two rooms, book a larger riad, or book a small riad outright, which a few allow.
Ask the details before paying anything. Is the family room on the ground floor or up steep stairs? Does it connect, or are the rooms on different sides of the courtyard? Is there a cot? How deep is the pool, and is it fenced? Courtyard plunge pools are rarely fenced and can be a hazard for toddlers.
If you need more room, hotels in Gueliz, Hivernage and the Palmeraie are generally better for families and groups: more rooms, bigger pools and kids' facilities. Many families split the stay, with a couple of nights in a medina riad for the atmosphere and the rest somewhere roomier.
Tell us the children's ages when you ask for a quote, and we can suggest family-room riads that fit.