Durin's Day on September 30?
According to the lunar calendar seen on the wall of Bard's home in Lake-town, the date of Durin's Day is 30 Halimath (September).
Link: https://img1.etsystatic.com/074/0/10713907/il_570xN.817148011_hxxx.jpg
Note that this only works for the film trilogy as in the book Durin's Day of TA 2941 would have been in the middle of October or later. Also, the moon observed by Bilbo on Durin's Day more closely resembles the one for the date of 5 Winterfilth (October) on the calendar. Nor does the midsummer's eve moon on the calendar match the one we see in Rivendell in An Unexpected Journey.
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