I have just done the 2nd birthday (with 4 year old guests too)

Pass the parcel was a bit touch and go. It worked because I had done a practice run through (much to the delight of my girls) the day before so the birthday girl (DD2) got it. For the other 2year olds, it worked with them sitting on a parents knee so that the mum or dad could help move the parcel along IYKWIM

The pull the string pinata was a hit with silly glasses, party hats and honkers falling out along with a few jellybeans.

We also played musical statues and did "we are going on a bear hunt". Both games were a huge hit.