Don't move the babies out. Just leave the parents to look after them. When cichlids are reared artificially instead of being left with their parents, they don't learn how to become good parents and regularly eat their own fry when they breed.
In addition to this, the convict cichlids will probably have 300+ babies and the shop will only take 10-20 from you. There is no point having hundreds of baby fish that you can't get rid of. Leaving the babies in the tank will let them be reared by their parents, and with any luck, the other fishes in the tank will reduce the number of fry you need to find homes for.
If you really want some for the shop, take out 20 or 30 babies when they start swimming around exploring the tank by themselves. They will be about 3-4 weeks old then and you can grow them up in a separate tank.