Please be aware that Tokyo has multiple airports and that these results are for all airports serving the city.
The best month to fly between Tokyo and Fukuoka is April and the most expensive month to fly is February. (Average prices, based on 263 datapoints.)
The best day to arrive at Tokyo is Monday and it would be best to avoid Thursday, as prices are on average 75.65% higher than on Monday. (Average prices, based on 254 datapoints.)
The cheapest airline flying from Tokyo to Fukuoka is Peach Aviation. They are 66% cheaper than Japan Airlines. (Average prices, based on 295 datapoints.)
The best time to fly is at around 7. (Average prices, based on 366 datapoints.)