Here are some more chants from this Greekchat.com's thread:
http://www.greekchat.com/gcforums/showthread.php?t=42998

My sorority has a first name
Its D-e-l-t-a
My sorority has two other names
Their D-e-l-t-a
So if you feel the need to chill
call *** **** (we added our tele#)
'cause gentleman prefer to say the date a d-e-l-t-a
(to the tune of the Oscar Meyer song!)
-GatoDnc7DeltaX3; 02-17-2007, 01:16 AM

**

We wear our pink pajamas in the summer when it's hot
We wear our flannel nighties in the winter when it's not
and sometimes in the springtime and sometimes in the fall
we jump right into bed with nothing on at all.
Here's to Delta Delta Delta
Here's to Delta Delta Delta
Here's to Delta Delta Delta
In the spring time and the fall with nothing on at all
Don't you wish that you could be there (x3)
In the spring time and the fall with nothing on at all.
-ilddd3; 02-17-2007, 03:46 PM

**

Delta Delta Delta
Who the heck are we?
We are the girls of the Deltas three
Go Delta!
Delta Tri Delta Tri Tri Delta Tri
Hey!
-RHITDeltaGal; 05-04-2007, 03:03 AM

**

Ba-doom Ba-doom
Tri-Delta
Ba-doom Ba-doom
Tri Delta
Ba doom Ba doom
Tri-Delta
Boom Boom Boom Boom
Delta DD
(descant)
Tri-Delta and you'll go the right way
Tri-Delta and you're here to stay
Tri-Delta and you will see
What a happy bunch of girls live in Delta DD
-estherjb 08-21-2007, 06:59 PM

-snip-

There are a number of other discussion threads at that Greekchat.com site which include chants and songs on some from White Greek letter organizations (WGLO) as well as Black Greek Letter Organizations (BGLO). It's interesting to see the similarities and differences between the structure and words of these two (undergraduate university based) Greek letter organizations. I'm aware that there are Latino, Asian, and multicultural Greek letter organizations. But I haven't found many of their chants/songs yet.