US Navy (and CINCPAC) communiques list six air raids on Funafuti:
N. D. COMMUNIQUÉ NO. 353, APRIL 23, 1943
South Pacific (all dates are, east longitude).
2. On April 22:
During the early morning, a group of enemy bombers raided Funafuti, U. S. occupied position in the Ellice Island Group. Light casualties to personnel were suffered and minor damage was inflicted.
N. D. COMMUNIQUÉ NO. 446, JULY 21, 1943
South Pacific (all dates are east longitude).
1. On July 20, during the early morning, three Japanese bombers dropped several bombs on Funafuti, Ellice Islands. No damage was reported and no personnel injuries were sustained.
N. D. COMMUNIQUÉ NO. 448, JULY 23, 1943
South Pacific (all dates are east longitude).
1. On July 22, during the early morning, Japanese bombers attacked Funafuti, Ellice Islands. Two of the bombers were shot down. Material dam*age has not been reported, but some personnel casualties were sustained.
N. D. COMMUNIQUÉ NO. 464, SEPTEMBER 14, 1943
Pacific Area (All dates are East Longitude).
3. On September 13, during the night, fifteen Japanese planes attacked Funafuti, Ellice Island. One enemy plane was shot down by antiaircraft fire. Material damage sustained was slight.
CINCPAC PRESS RELEASE NO. 168, NOVEMBER 13, 1943
Early this morning (13 November west Longitude date), six Japanese bombers raided our installations on Funafuti, Ellice Islands, dropping about thirty bombs in two high‑altitude runs, causing minor material damage. Per*sonnel casualties were two wounded.
CINCPAC PRESS RELEASE NO. 170, NOVEMBER 18, 1943
About 10 enemy bombers made a medium altitude raid on our installations at Funafuti, Ellice Islands, before dawn on 17 November, West Longitude Date. Our losses were two killed and several planes damaged.
East longitude dates are one day earlier than local dates.
There were other actions were Japanese planes get close to the island:
_ on 27 March 1943 six Japanese bombers were detailled but were intercepted by VMF-441. One was shot down, the other turned back. Details are available here:
http://forum.12oclockhigh.net/showthread.php?t=33456
_ on 10 September 1943 the 5th Marine Def Bn reported engaging an Emily. See
http://www.fold3.com/image/251/270143676/ (my fold3 account is now down due to a change of credit card, so I can't check the content)