I am quite sure that the number 1 reason why you chose to rent a house over buying a brand new one is the price or cost of it. If you have a very limited money or monthly budget at hand, renting a home is definitely the most applicable one for you to choose.
In choosing houses and homes for rent, you have to keep in mind that you must get the best quality and comfort out of your budget. It seems like an impossible task but its doable. You just need to search and ask more than the usual. You have to talk more with your landlord on how you can work it out (in terms of rental fee).
If the landlord said no in terms of lowering down the rent to make it good for your budget, ask if there is something you can do in return (either service or help for their business/house) that can give you some sort of discount in terms of renting. Maybe, if you work as a plumber or something into those kind of like of service, you can ask your landlord to just make you as their personal service man in return of huge discount from your rental fee.
One more thing to ask is, if there is anything that they can remove or pull out from the house that can lower down your rental fee. If they said yes and you find it not so useful for you and your family, by all means, make them pull it out.
As you can see, some of the tips I gave seems like pretty impossible to happen. But, if you will just ask and ask more (in a good and gentle manner), your rental fee can surely meet your budget.