If there are four of you I'd recommend a taxi to Diani. I'm not exactly sure what you'd be charged but the rail station is a little further than the airport, and airport-to-Diani transfers typically cost around 50 USD.
As for public transport, at the station you'd probably be pointed to a minibus into Mombasa but you'd then need to take another minibus, a ferry, one more minibus and then a tuk tuk, to reach your Diani resort. Not worth all the hassle in my view.
There's 2 options:
1. Taxi ( from out side the Terminal )
2. Hotel Transfer - are you staying in a hotel ? If so, ask the Hotel for transfer.
If you don't have much luggage, you can board the Ferry on foot & take another taxi from other side to Ukunda.
During peak hours, it can take upto 1 hour to board the Ferry.
Taxify estimates the trip with 1800-2200 KSh. Has anyone tried this? Is it realistic?