Jodafett – a WeeRide when they’re small nd a LOCT when they get bigger. Both mount from seat post and a t the back end, but are dropper compatible (better with a dropper I’d say) and the LOCT goes on the steerer tube at the front (replace 10-15mm of spacers) while the WeeRide goes to the head tube (around 3mm of head tube needed above the top tube, but you might get way with less).
LOCT is a better seat, but a) only for 2 to 2 1/2 year olds upwards and b) like gold dust now (ask nicely on here for second hand ones and someone might have one) though they may come back into production some time.
LOCT website
WeeRide is not as good (though perfectly acceptable) but does younger children and is readily available.
WeeRide website
Both are better for taller riders as he child sits in front of you.
The pay off is that the weight is central and within reason you can still ride most stuff – certainly 90% of rail centre reds.
EDIT: dropper is good with a child seat as you can get on and off the bike with the saddle down – ie both feet flat on the ground.