OK, I can remember some names. In Poppies 1, Kedin Inn is well known, has been there for years, is often pretty full, but give it a try. Some info here
Accommodation on Poppies Lane I Kuta Bali | Bali Blog
Nearby to it are others, not quite so famous, but offering similar deals.
In Poppies 2, there is Tunjung Bali, see here
Tunjung Bali Inn - Reviews and Cheap Rates - TravBuddy
and nearby to it there are other similar places - Bali Sandat 2 is just behind it and very similar.
These places are offering low prices, and I would not expect much discount for longer-term stays - but you can ask. For me, fan rooms are OK, and air-con is not really needed.
I have not found any of these places to be noisy, and mostly the rooms are large and clean. Both Poppies Lanes are congenial places to stay with plenty of cheaper cafes, bars and convenience stores. If you have a car - parking may be a problem at some of them - but for motor-bikes, no problem.