In reply to featuresforfeet:
I've been cycling round Jersey for 30 years (I have family there). It's unique, and wonderful. I'd totally recommend it. No reason why you shouldn't take a child on a child-seat, if you're used to the extra weight and the change in your balance set-up. Get a bike with plenty of gears--there are some surprisingly meaty hills, e.g. out of Bouley Bay, and the roads often have short sharp climbs, even though nothing is all that big. If you want to go on rough lanes or the north coast path, get fat tyres. Don't cycle on beaches unless you want to lose your hire deposit; don't cycle on pavements unless you don't mind an on the spot fine.
Jersey has lots of Green Lanes where traffic is either non-existent or minimal. You can get a cycling map of Jersey that marks them. Especially with a child on board, you might wish to avoid the A roads, which can be busy, and aren't always very wide.
I recommend Zebra Cycles, in St Helier just by Liberation Bus Station. https://www.zebrahire.com/bikes/ Or there's a place in St Aubin, at the beginning of the old-railway cycle-path to Corbiere.
That's one of the easiest and safest excursions to do, incidentally--head out of town towards St Aubin along the esplanade, then in St Aubin go up the lane that gets you on to the cycle-path. Then just cycle to the lighthouse at Corbiere. (Watch out where the cycle-track crosses roads, which it does about 5 times.)
Going the other way from town, there's a cycle-path through the middle of the island to Gorey, but it's hilly. Or you can cycle the coast road, which is very pretty, but fairly busy as far as Green Island. Then there's an excellent boardwalk cycle-route up past the German Hospital in the middle of the island: you can go north on that to St Mary or St John, then turn around and come back down one of the other valleys.
More ambitiously--and probably best not to do this with a child on the back--there's the cliff path on the north coast, which is simply magnificent.
The Tour de Jersey (always taking the continuous road that's nearest the sea right round the island) is a wonderful ride; it takes me about 3 hours, not that I hurry it.
Post edited at 14:14