Iberia go daily or more from Majorca to Rome. good website.
Also check out Air Comet, though one can't tell if any smaller airline exisiting today will be around tomorrow.
Can't help with price unless you say dates.
Also -and as a travel agent I hate to say this....
Ryanair go every afternoon from P.de M to Girona and every evening from G to Rome- a few hours connection in girona .
(remember - Ryanair don't have connecting flights .Each flight is seperate. If one Ryanair flight arrives late and you miss the next Ryanair flight, that's tough)
As I dont know your dates I cant say price but in june on many days I note that you can do both flights for total of about fifty euro inc. taxes. But ,sorry, add bags
It's only worth doing Ryanair if Iberia are full or costly.
there's also Ryanair flights from ibiza to rome
Obviously getting from Dub to P de M and from R to Dub is with either Lingus or Ryan.