If the lower sink is a 2" line, you should be able to wye in below the sink and run a two inch pipe up. You will also need a p-trap for the washer and vent it.
I am planning on installing a washer and dryer in an 1st flr closet. The existing washer & dryer are in the basement. The washer drains into a basement sink. Can I run 2" pvc drainage pipe from the closet to the basement sink? Is this an acceptable code wise in any state? Or do I have to make a connection into the waste stack?