It's not the verb tense you use, but rather you need additional words to convey whether it's regular or not. If it were a regular, weekly lesson, you could say
"Tim and Jim can't go with me next Sunday. They're having one of their singing lessons then."
If it were a one-time lesson, you could say something like
"Tim and Jim can't go with me next Sunday. They signed up for a singing lesson that day."
(not a teacher, just a language lover)
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