I really don't know any place that fits in your budget.
The cheapest hotels I know are around Quatre Bornes (forgot the name of that hotel). Also in Mahebourg there are some low cost family pension.
still, all of them are more expensive than the budget that you mentioned.
Though, seen the budget that Mauritian workers have, I think it could be possible to find something - but you certainly won't find it in the internet.
I would suggest to you: get a reservation for the first days of you stay in a cheap hotel/pension, and try your luck once you've arrived.
Ask everybody you meet, walk around the town for 2-3 days, and just ask everybody.
Mauritians are quite easy to talk to, and I often have been asked in the streets, if I need some rentals.
I think you can manage it somehow to find something that will fit your budget