A while back I wrote an article for a re-enactment group called the Ship's Company. Here is an excerpt from that article.

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I've attached a photo from Miller's The Photographic History of the Civil War.

Look very carefully at the seated sailors. From what I can make of the photograph we have:

1. a vocalist, perhaps a dancer or bones player
2. something or other with a neck (I don't see frets so I'm going to guess banjo)
3. a banjo (Will you look at the size of the body on that thing?)
4. a guitar
5. a fiddle
6. another fiddle
7. something that isn't immediately obvious (Wait for it.)
8. another banjo (Can't have too many banjos, right? Kind've a long neck on this one; a bassjo, perhaps?)
9. what looks like the bow to yet another fiddle and the dimmest outline of said fiddle tucked in his left arm
10. another vocalist and/or dancer and/or bones player (Look very carefully at the way he's holding his left hand. There might be bones between his fingers.)
11. and -- brace yourself -- a bodhran player?!? (There's something large and circular under his left arm. I don't think it's a bass tambourine.)

I submit that the sailor seated seventh from the left has a two-row button accordion tucked underneath his left arm. The reasons I believe this are:

1. It's tucked underneath his left arm in exactly the same position I hold my button accordion when it isn't strapped to my chest.
2. The instrument is positioned so that a fair amount of it would be able to extend/project behind the banjo player in position eight. This arrangement allows the accordion player room to open his bellows without interfering with the sailor on his left.
3. The accordion player has his right hand placed so he can start playing when the music starts.
4. The instrument is on his left knee so he can start playing when the music starts.
5. That (relatively) wide white smear is what the "keyboard," looks like in a grainy photo.
6. As I recall, the photo in the book (as opposed to the picture from the cited reference) shows two rows of white buttons in a staggered arrangement. To the best of my knowledge there's only one instrument with that kind of configuration namely a two row button accordion.

Reference
Miller, Francis Trevelyan. "The Photographic History of the Civil War (Volume 6: The Navy)." The Perseus Digital Library.
    Monday, May 19, 2008 7:42:24 PM. Tufts University, Medford, MA. 19 May 2008
    <http://www.perseus.tufts.edu/hopper/text.jsp?doc=Perseus%3Atext%3A2001.05.0111%3>
    (If that URL doesn't work try <http://tinyurl.com/43hy96>.)