Ragnar has spices you can trade for with sugar - you have some unhappy in a few cities. You can also renegotiate your sugar deal to Alex to get an extra 4 gold/turn.
Military wise - Ragnar has 3 cities, he'll be a pushover. A good approach is to whip (in cottage cities whip mines/unmatured cottages - keep farms/food) 15~20 cuirassiers (depends on Alex's power), focus espionage on Alex. He's pretty big (12 cities well spaced out) so I'd do it in 2 waves. Do it fast while you have a tech edge.
The first wave would be to revolt Sparta, and then take take it on the first turn of war. Unfortunately he hasn't built the shrine so Argos isn't high-importance. Also in the first wave, he'll bring in his SoD (which you want to find out before the war by scouting). Keep a sentry to monitor its movement and take it out in the field, should be easy. Take peace for techs if you can or a Cease Fire. Doing so will allow you to redeclare ASAP when your stack is healed. Ragnar might send 4~5 units your way too so keep a few units with cleaning duty. If your stack is ok or you have a super-medic, try to take out a few more core cities (Athens, Halicarnassus).
The second wave, all you have to do is take the rest of his cities. He'll offer barely any resistance. You will perhaps have teched towards rifling, if so it'll be even easier.
Your economy will hurt a bit, but afterwards you'll have so much land (and his land is pretty well developed), all you need to do to win is tech Democracy.