I've planted radishes in early march and had good results with them growing. If a few get frozen there are typically enough to still have a good crop. Radish seed is also pretty inexpensive in bulk.
Another trick we use is to plant a light crop of radishes over the top of carrot seed. This is a good marker for where the carrot seed is planted. The carrots germinate slowly and are just coming up when the radishes are ready to harvest. The radishes provide some protection for the tiny carrots and are easily harvested or eliminated if they are not needed.
Don't forget to plant succession crops every few weeks. Most people assume that radishes don't grow in the heat of the summer. But we have had good luck growing them in compost with adequate water. They need to be harvested before they get too large or they can get hot.
Radishes are very fun for young children to plant and pick. Even if they are too spicy for young tastes they are still a lot of fun to grow.
Radish seed has very long germination so you can buy bulk ahead and save. Get enough for 3-5 years and you should be fine.