The speech marks are definitely there, as is the apostrophe after the letter 'o', which means that the chances are Donald Emson's mother intended us to understand that this is a quotation rather than simply a term of endearment. But a quotation from what? My best guess is a poem called Boy O' Mine written by the American poet, Edgar Guest (1881-1959) and published in a collection of his verse called When Day is Done. The last verse could have resonated with Mrs Emson:

Boy o'mine, boy o'mine, this is my prayer for you;
Never may shame pen one line of despair for you;
Never may conquest or glory mean all to you;
Cling to your honour whatever shall fall to you;
Rather than victory, rather than fame to you,
Choose to be true and nothing bring shame to you.

The poem was not published until 1921, which may seem too late to be used as a source for a headstone inscription. However, many war cemeteries were not constructed until the late 1920s so this is not necessarily a problem. A slightly bigger problem comes from the fact that there appears to be no evidence that either the poem or When Day is Done was ever published in Britain.
There are other contenders but they are equally American and even more unlikely. Soldier Boy O' Mine, written in 1919 by Elizabeth S Howe has a first verse that goes:

All my heart is with you o'er the ocean
In my dreams your dear face I can see
And I long for the day, when from far away
You'll come back to the homeland and me.

Somehow this doesn't sound like something that would appeal to a bereaved mother. And there's another poem with the title Boy O' Mine, words and music by Florence T Irving, which was written in 1918:

Just a song boy o' mine
Just a message of love
Just a prayer oh boy o' mine
To our father above ...

But the subject of the song is really the Stars and Stripes so that rules it out for me.

Donald's father having died when he was four, his mother supported herself as a school teacher. Donald, a farm labourer, volunteered and went out to France in September 1915. In September 1918 he was in Salonika with the 9th Battalion The King's Own Royal Lancaster Regiment, which took part in the costly assault on the Grand Couronne and Pips Ridge near Lake Doiran on 18-19 September. Emson was killed in action on the 19th.