It occurs to me... Why don't they ever include a musical instrument in sentences with "suonare"? That would make the difference between "giocare" and "suonare" a lot clearer.
An object would be necessary for ring to apply here. You could ring the bell on Sunday, but there is no bell in this sentence, so the best translation is play (a musical instrument)
I thought that a phone was implied; as in, "we will ring you up (call you) on Sunday"