In reply to ADJ85:
Just to add to the posts below, noting your profile and profile pic and throwing in my own recent experience of two year olds and earlier experience of kids at crags in Cornwall from the age of 4 upwards.
Short answer is I can't think of any roped climbing place in the west of Cornwall that would work if you've got a two year old. Trewavas, Sennen and Rosemergy in particular just don't work and Roche, which isn't in the west, is dull apart from the rock itself.
Hence my suggestion of bouldering at Godrevy rocks, at the extreme right hand end of the long beach I think of as Gwithian (I am at terrible at names). There are lovely canyons between the rocks where you can boulder while the tots pootle about at the bottom with rock pools and a sandy beach to amuse them. The car park is adjacent and there are nice cafes and also an impressive haul-out of seals nearby.
When we had a clutch of kids from 8 upwards we used to camp near Porthguarnon cove and one time took them scrambling there for an adventure, out along the bottom of the crag and then up, somehow. We also did a roped climb there, a diff I think. A photo of that is on my profile.
Take the two year old (and one adult) out of the picture then lots more comes into the frame especially if there are still two adults left over. Just getting the kids along the base of Bosigran and then scrambling up out at the end is wonderful fr them, and if there are two grown-ups, doing the first pitch of Alison Rib with the kids is fun.
Another thing you can do, that I did when my daughters were 4 and 7 or so, is just to go boulder hopping on beaches. It is a lot of fun to do that between Trevellas and Trevaunance coves at St Agnes, for example. You can also have an adventure a little bit further along by going at low tide along the sandy beach from Chapel Porth towards Porthtowan and then, just before you get there, escaping upwards the coast path.
Around St Agnes Head you can also descend from the coast path onto Tubby's Head, scramble around and get really quite close to the sea. It feels like a wild old place (see another of my profile photos) that I think would thrill kids inclined to be thrilled. In that vein, it is also quite a fun thing to walk out all the way past Right Angle, right to the end of Gurnard's Head and then back.
Anyway, have fun!