The church you mean is Daimyomachi Church in Daimyo, and its official access points to Tenjin Station, not Hakata. The address is 2-7-7 Daimyo, Chuo-ku.
For Fukuoka's historic centre, the choice is Hakata Station or staying on the Airport Line to Gion. Tenjin looks like the main downtown hub but is the wrong way.
From Kyoto Station, the Karasuma Line to Imadegawa plus bus 203 to Ginkakuji-michi takes about 43 minutes. Weekend EX100 runs from stop D1 to Ginkakuji-mae.
Since the 14 March 2026 revision every Nara Line rapid stops at Inari: two stops and under ten minutes from Kyoto Station, the main torii opposite the gate.