There may be a M.Y. answer on this one - a hunch.
Two that occur to me offhand are:
The bracha for lighting candles before Yom Kippur .להדליק נר של יום הכפורים
ברכת האלנות - The bracha upon seeing fruits bloom on a fruity tree may be said only once yearly. I'll add in halachic source, later.
I got these from a yeshivanews.com page:
על ביעור חמץ upon inspecting for chametz.
נחם ציון ובונה ירושלים said on Tish'a B'Av
(Thanks to DoubleAA for the help on these two:)
It is possible to say the bracha for Eruv Tavshilin just once per year, such as this year (5779) when 7th day of Pesach is on Friday, in Diaspora.
In Israel, it could occur either when 7th day of Pesach is on Friday or the 1st day of Shavuot is on Friday, or the 1st day Rosh Hashannah is on Thursday.
It is possible to say המבדיל בן קודש לקודש once per year, also. This occurs only in Israel when either the 1st day of Pesach is on Sunday or the 1st day of Shavuot is on Sunday.