Bad tenant ledger- How do we rent ever again?

Hello. My family and I are currently renting a house. We have been in arrears before with the rent, but have since caught up. We know the landlord, and she/he will not give us a good reference. I'm looking at moving out and finding another rental, but how do you get around the "request for rental reference" thing? The new real estate agent will see our tenant ledger and it looks bad. (even though we don't owe anything) Does anybody have any advice? THANKS.