In addition to "Hail Godlike Washington," posted by rich r above, there're other Washington's birthday songs to the tune of "God Save the King."

Americans rejoice,
While songs employ each voice,
Let trumpets sound.
The thirteen stripes display,
In flags and streamers gay,
'Tis Washington's birth day,
Let joy abound.

From scenes of rural peace,
From affluence and ease,
At Freedom's call;
A hero from his birth,
Great Washington stands forth,
The scourge of George and North,
And tyrants all.

The silver trump of fame
His glory shall proclaim,
Till Time is done.
Genius with taste refin'd,
Courage with coolness join'd,
'Bove all, an honest mind,
Has Washington.

~~~~~~~~~~~~~~~

Long may he live to see
This land of Liberty
Flourish in Peace;
Long may he live to prove
A grateful people's love,
And, late, to Heaven remove.
Where joys ne'er cease.

Fill the glass to the brink,
Washington's health we'll drink,
'Tis his birth-day.
Glorious deeds he has done,
By him our cause was won,
Long live great Washington,
Huzza! Huzza!

SOURCE: Vera Brodsky Lawrence, Music for Patriots, Politicians, and Presidents (Macmillan, 1975, p. 96)

~Masato