I live near coniston, and there are lots of things to do, but some will require getting in the car.
In around coniston: there is a small playground on the road that goes to the boat hire, there are also several walks around the village and up the fells-it is worth looking into a walk to the copper mines, but you might need a rugged buggy for that one. Also- i would take the steamer over to brantwood and walk the gardens there. Doubt two year olds would enjoy ruskin's house, but the gardens are lovely and good for a game of chase (the gardens also have fencing to keep lo out of the road).
Near coniston: Check out the lakes aquarium in newby bridge, the motor museum in backbarrow, and playzone in ulverston for indoor fun
For outdoor there is a great park at fell foot on lake windermere, and loads of stone circles to explore.
Just remembered- it is a bit further away, but if your two year old is as obsessed with thomas as mine, there is the ravensglass/eskdale narrow gauge steam train. My very very active lo sat in complete awe the whole journey! M