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Both Paphos and Larnaca airports are convenient for Limassol. Depending on where you are staying in Limassol they are both around 45 minutes away by car. If you need to use public transport it is probably more readily available at Larnaca than Paphos, although it is possible to get from Paphos to Limassol on public transport.
http://www.luxorlimassol.com/gpage1.html This link gives lots of information regarding transport from the airports.