Honestly, any of the major cruise lines ships built in the last 10 years will do as you wish (stable). All have active stabilizers, which are wings below the water line that extend in open water to reduce rocking.

One of my favorite stories I tell my "Cruising would make me seasick" friends is when my wife and I were sitting in the bar on the Holiday (considered tiny by todays standards) wondering when the ship would leave. We went up-top to see what the delay was and realized we had been at sea for 30 minutes. We hadnt felt a thing! Of course if you get caught in bad weather...Size doesnt matter.

Be forwarned though...her first cruise wont be her last. You may get her addicted!