Once my students have their lyrics, we work first on rhythm. Sometimes they have a melody simultaneously, but not always. So I have them chant the words in the rhythm they think is best for the song. One pitfall to watch out for is “monorhythm” — that is, everything in quarter notes or eighth notes. Occasionally, this is okay for some of the song, but rarely. It sounds robotic — at least in English. It is extra challenging with the students I presently teach, because in Czech, all words are accented on the first syllable. Many of their children's songs have extended monorhythmic passages — if you know Kodály rhythm syllables, then they are like so:
"Prší, prší": | ti-ti ti-ti | ti-ti ti-ti | ti-ti ti-ti | ti-ti ti-ti | <— e.g. this whole first line | ti-ti ti-ti | ti-ti ta | ti-ti ti-ti | ti-ti ta | <— this one is more like "Twinkle, Twinkle"
Often what is better is to try to speak the lyrics in the same way that you would say them if you were talking to somebody. This naturally creates a more interesting rhythm. Another thing to make students aware of are the accents in the language — not every syllable has equal emphasis — and how those accents generally line up with strong beats. There are many ways to create exceptions to this rule, using syncopation and length (agogic accents), but I do not usually point this out to beginning students. Some students figure it out naturally, because of the music they are listening to, some do not. I give gentle guidance: if it works, I leave it alone, of course; if it sounds awkward, then I point that out and we figure out how to fix it.
After we have created rhythms, we start trying to create melodies. I start by having them again say their lyrics with the rhythms they’ve chosen while playing the chords to the song. I have them simply try singing and then I sing it back to make sure that’s what they want. If what they sing is not in the right key, I sing the same shape they sung, but in the key that we are in. Here, one the pitfalls is that the whole song is only chord tones. The good news is that it means the student hears the chord tones! But unless it’s “Reveille” played on a trumpet, songs are rarely only chord tones (although I noticed one other famous exception recently: “The Wheels on the Bus.”). It’s important to balance leaps and steps.
If students have a hard time audiating a melody (whether it's in the key or not), then they have the option of using Boomwhackers/tone tubes, a glockenspiel, or a piano — for the latter I draw a diagram of the keyboard and label the pitch names. If I had Orff Schulwerk instruments, I would use those, but we work with what we have. The pitfall with this is that the melodies are often very random and have too many leaps. It's a sign that the students still aren't audiating, and often that they can't bring themselves to care.
I think that lack of care is actually a defense mechanism. We are always dealing with a certain level of vulnerability, particularly with middle school students. It's an age where we still do not have real power over our lives, but we are starting to figure out what we are "good at" which is the beginnings of some power and control, as well as sources of social connection. People do not want to be put in a position where they are seen as incompetent. Some students don't mind, but this is a choice, and a certain kind of power, too, this ability to not care what others think. Making a melody — and heaven forbid, having to sing it also! — is something personal that is made public, that doesn't happen in classes like math or even language. It's a very vulnerable situation and I often get pushback from the students.
I notate what the students come up with because it helps me remember their song and it always looks nice to see your music in print — it’s a small joy, but the students really are impressed. I also perform and record their songs so they can hear and remember what it sounds like, since we only meet once a week. For ukulele/songwriting I do not emphasize literacy in the way I do if I’m teaching beginning band instruments. It takes a while — years, in fact — to really assimilate reading notation with your hearing, just as it does for reading language. So in the same way that we expect children to spontaneously speak, but not to spontaneously write, we can expect music students to spontaneously make sounds in a tonal context accurately before we can expect them to read or notate what they hear.