We do not have a pick-up service, but there is a shuttle service from Kansai airport to mostly anywhere in Kyoto offered by MK Taxi called ‘Sky Gate Shuttle.’ Please see this link for more information.
https://www.mk-group.co.jp/english/shuttle_kyoto.html
Here are other transportation options from Kansai Airport to Kyoto station. Either of the train options are recommended but the bus also runs often and offers early and late departures.
JR Haruka Limited Express Train
2,850 yen for non-reserved seating
3,370 yen for reserved seating
(approx 80 mins.)
Departs approx every 30 minutes from Kansai Airport (operates daily from approx 7am to 10pm).
https://www.westjr.co.jp/global/en/travel/shopping/access/train.html
JR Regular Train Service
1,880 yen (approx 100 mins.)
Take the JR Kansai Airport Rapid Service train to Osaka station (approx 70 mins,). From Osaka station, take the JR Tokaido or JR Kyoto line to Kyoto (approx 30 mins.). Departs approx every 15 minutes from Kansai airport (operates daily from approx 6am to 11:30pm).
https://www.westjr.co.jp/global/en/travel/shopping/access/train.html
Airport Bus Service to Kyoto Station
2,250 yen (approx 88 mins. from Terminal 1, 103 mins. from Terminal 2)
Buses depart roughly every 20 minutes. Departures for Kyoto are from bus stop #8 at Terminal 1, or bus stop #2 from Terminal 2.
https://www.okkbus.co.jp/en/timetable/KY/#from
Flat-fare Taxi Service
15,000-17,000 yen per vehicle (approx 85 mins.)
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Please see this page for a recap of the information above.
https://www.kyotostation.com/traveling-between-kyoto-and-kansai-international-airport/