This is:

YMCA Founded in London

George Williams founded the Young Men's Christian Association in 1844.

What else? It's fun to stay at the Y-M-C-A!

D-Day in World War II

150,000 soldiers in the Allied Expeditionary Force land in Normandy, France.

You could feature songs from the 1940's and patriotic traditional songs. Two that I might use are "Ac-cent-chu-ate the Positive" (a WWII morale-boosting song) and "Boogie Woogie Bugle Boy of Company B".

Number 1 Songs

Songs that were number 1 on June 6 that I know have square dance versions:

• 1956 - Standing on the Corner by The Four Lads
• 1956 - Blue Suede Shoes by Carl Perkins
• 1965 - Wooly Bully by Sam the Sham and the Pharoahs (actually there's a patter record that uses the main riff from this song)
• 1992 - Achy Breaky Heart by Billy Ray Cyrus

June is:

National Accordian Awareness Month

National Accordion Awareness Month was established in 1989 to promote the accordion, help spread the word about the resurgence in popularity in the accordion and to educate people about the accordion. Here's some info.

I'm sure there are bunches of (old) square dance records that feature the accordian. I tend to associate MacGregor with accordian arrangements.