Children now outgrown them, but we had 2 different ones. First a Hamax, the exact model is no longer around but the current ones are very similar and there is a link to one above. We went for the non-reclining version. That had quite a heavy bracket bolted round the seat tube into which the twin prongs of the metal support arms of the seat fitted. Nifty button system to show they were locked in and the seat was then cantilevered over the rear wheel on the support arms. Gave it a bit of suspension but sometimes had a slightly unerving amount of bounce, although it got round the green and blue at Dalby with no mishaps. Left you with a heavy bracket on the seat tube that took a bit of time to fit and take off again so tended to leave it on what was basically a hack bike. No attachment to the seat stays so no issues with fiddly fittings but, whereas on my 20 inch frame the bracket came halfway down the seattube, on my wife's 14 inch frame it would have fouled the front mech so that led to plan B – a Co-pilot Limo.
This fits on a Blackburn EX1 rear rack which is included in the price. The rack is a bit of a pain to take on and off but the attachment seemed a lot sturdier albeit straight over the back wheel and with no in built give. On balance for offroad I would probably feel safer with the co pilot but both company's products seem fine. The Hamax are a bit cheaper ( although they do their own rack mounted system that is about the same cost as the co-pilot – sorry got no experience of this, only of the seat tube mounting version ).
One issue to check on is the fit of the Blackburn rack. You will need the frame to have rack mounting points -obviously- and on my wife's very small frame I needed to get some longer strips to join the front of the rack to the seatstay mount points. There are a number of posts around including a review on Wiggle that say it won't fit bikes with disc brakes, and although it is a standard rear rack and SJS cycles and CRC seem to think it will fit most bikes I found a posting on a US forum that quoted Blackburn as saying they didn't make bikes for frames with disc brakes and didn't approve of the much posted fix of putting in a cylindrical spacer between rack and frame.
I think Madison import Blackburn so they should be able to give you the official view.
Last point is make sure you tie the little blighter's feet into the foot stirrups with the straps provided or there is a risk of them trying to insert foot into spokes. On balance I suspect the spokes will win.