Here's another some of us like. It's sung in the 1970 film, The Railway Children; the song is from Edith Nesbit's 1906 book on which the film was based. The birthday girl is named Roberta, so any birthday person's name would be substituted in for her name.

Our darling Roberta,
No sorrow shall hurt her
If we can prevent it
Her whole life long.
Her birthday's our fete day,
We'll make it our great day,
And give her our presents
And sing her our song.

May pleasures attend her
And may the Fates send her
The happiest journey
Along her life's way.
With skies bright above her
And dear ones to love her!
Dear Bob! Many happy
Returns of the day!

About the text - E. Nesbit writes, "Roberta knew that Mother had written the words on purpose for her birthday." One would assume that Nesbit is responsible for the words, but there is some indication that she used an older source, John Hartley's Halifax Almanac (known as The Clock Almanac), first published 1865. I can't find good info on that possibility online.
The tune Nesbit specifies in the book is "the first part of the tune of St. Patrick's Day." This is the tune: "St. Patrick," 1902, by Charles Villiers Stanford, b. Dublin, Ireland (1852-1924).
St. Patrick (Stanford)