There is a second version of the song which has a different tune and chorus, but uses the same verses (guitar chords included):
E D A Am (or) Eadd9 Dadd9 Aadd9 Cadd9
E D A
Jesus loves me, this I know,
For the Bible tells me so,
Little ones to Him belong,
They are weak but He is strong.
Alleluia, allelu(ia) (repeat)
All the verses from above are easily sung to this tune; verses from other songs also fit the tune as well (e.g. Amazing Grace). This version is often found at summer camps, and sung around campfires.
As the author of this song died in 1915, I will assume that it has moved into the public domain. I shall attempt to create a 'tune description' for this version in the near future to help any interested in singing this version.