It's often difficult to spot which is a children's rhyme and which an adults, as parody is often used as a political device for supporting and debunking famous figures.
There is one about Abe Lincoln based on the old ballad of Lord Lovel which begins:

1 Abe Lincoln stood at the White House Gate
Combing his milk-white steed,
When along came Lady Lizzie Tod,
Wishing her lover good speed, speed, speed,
Wishing her lover good speed.

2 Where are you going, Abe Lincoln?' she said,
'Where are you going?' said she;
'I'm going, my dearest Lizzie Tod,
O'er Richmond for to see, see, see,
O'er Richmond for to see '.

3 'When will you be back, Abe Lincoln?' she said,
'When will you be back?' said she.
'In sixty or ninety days at the most,
'I'll return to my Lady Lizzie, -zie, -zie,
I'll return to my Lady Lizzie '.

4 He hadn't been gone more than one or two days,
O'er Richmond for to see,
When back to the White House Gate he came,
All tattered and torn was he, he, he,
All tattered and torn was he.

5 'How do you flourish, Abe Lincoln?' she said,
'How do you flourish,?' said she.
'The rebels have killed my old Scoch horse,
And I have skedaddled, -dee, -dee, -dee, -dee,
And I have skedaddled, -dee, -dee.

6 Abe Lincoln rode his Burnside horse
Which started at the rebel's fire.
He threw the baboon heels over head,
And there he stuck tight in the mire, -ire, -ire,
And there he stuck tight in the mire.

Jim Carroll