You could take them to the upstream end, by the Tram Bridge, which is much quieter. Just above the Tram Bridge, there are steps down to a short stretch of flat concrete bank below the wall - you can't see it from the road. Both free fishing.
Under 12's fish Notts Fed waters free, so although you might cop for a day ticket (I've never had to pay) the Canal from Lenton to the confluence above Trent Bridge is full of catchable small fish. You can access from near the recycling centre at Dunkirk, from the cinema car park near to it, from Castle Marina, from near the station or from by the Trent Navigation pub on Iremonger road. The towpath gets pretty busy, though, as do most places around town. Here's a wild card - drive along the river past the Forest Ground, past the rowing clubs and park at the end just before where the Grantham Canal comes into the Trent. Walk a few yards down to your right, and you'll be on the canal where nobody will pay any attention to kids fishing. Alternatively, from the same parking place, walk 50m down the river and there's a level concrete bank running down to Lady Bay Bridge, also free fishing.
If you're keen on somewhere safe and peaceful for the children, though, you might conclude a day-ticket fishery fits the bill. The Nottingham Canal is deep and flowing, as it's really just a diverted length of Trent water. Tim Aplin, Matchman Supplies, West Bridgford, used to have copies of a long list of fisheries in the area for when people came in asking where they could take children.
