"ohayou" (おはよう) is used for "good morning".
"yoi tsuitachi" simply sounds like something stupid Google Translate would come out with! :P
If "yoi tsuitachi" were actually a real thing, it would mean something like "good first day of the month"...
I've never heard the reading "yoi tsuitachi" for 良い一日 before. I have heard the reading "yoi ichi nichi" in the phrase 良い一日を (have a nice day).