If your plane arrives after 8:40pm your choices are private transfer, car rental or to stay in Sapporo city or Chitose city for the night. The last bus departs the airport at 21:30.
If your plane departs before 11:45am it is possible to catch a train to the airport. The earliest train departs Kutchan station at 5:22am and arrives at the airport around 8:30am. (You will have to take a taxi from the Niseko Resort Area to Kutchan Station.)
Skybus has a private transfer option to the airport.
Staying a night in Sapporo city or Chitose city and taking the train to the airport in the morning is also an option. From downtown Sapporo city to Chitose airport the fastest and least expensive way to get there is by train. The cost is 1,040yen for adults. The earliest train departing Sapporo station to Chitose airport is at 6:00 am, arriving at the airport ay 6:48am. This will leave you enough time to check in comfortably for domestic flights departing as early as 7:30am.