Executive summary: the sparrow is the lover, and the robin is the child [thank you @PeterShor for cutting through the undergrowth]. Which might well invalidate my interpretation below :o)
Why a robin?
If you go here you'll find a link to a sample of robin birdsong, with the narration [emphasis mine]:
Unusually among British birds, both male and female ...
There's a substantial body of evidence that the title "Songs of Innocence" points to the fact that the poems were intended to be sung.
In the article William Blake and the Music of the Songs, Kevin Hutchins outlines several pieces of evidence for this:
The romantic period sought to draw on the historic connection between music and poetry. As Hutchins ...
Let's start by listing the titles of all the Songs, and noting that you can read them in full here.
I'll now discuss various possible pairings among these poems, but bear in mind that there's no definitive answer to this. Arguments could be made for many different ways of pairing up, and we're never going to have a perfect bijection. It's almost an exercise ...
There are actually two "Chimney Sweeper" poems: one in Innocence and one in Experience.
You can see them both in the full text of Songs of Innocence and of Experience, by Ctrl+F'ing for "chimney". The Innocence one which you're asking about runs as follows:
When my mother died I was very young,
And my father sold me while yet my tongue
Could scarcely ...
The resemblance is mostly thematic.
According to Bono (lead vocalist and primary lyricist of U2), the main thing they took from Blake was the idea of comparing innocence and experience:
I try not to talk about William Blake too much because it sounds pretentious quoting such a literary giant but it was his great idea I pinched to compare the person we ...
This almost certainly has to do with the technology of printing, and the economics of publishing.
There are currently many modern editions of Blake's illuminated works, and they contain much detail and many colors. To the best of my knowledge, the printing technology for mass reproduction of complex color images wasn't readily available:
Alois Senefelder, ...