Getting a Loan with no credit history

I am not a lender, but I do not think that they can get a mortgage without a credit history. They would also need a work history in this country to qualify. Zillow has a mortgage calculator here that might you run some numbers. It sounds like they have a down payment. The minimmum FHA requirement is 3.5% down.

Honestly, it does not sound like your parents are ready to buy. I can also hear the emotional conflict in your post about co-signing for them. Maybe you would consider taking a piece of anonymous internet advice from one poster to another. Please do not co sign for your parents. They are not ready to buy and you are risking your family relationship by cosigning for them. Instead help them build their credit and support their goal of home ownership. Make up an excuse, lie if you can't tell them the truth, but do not co-sign. Your relationship is more important than any tax credit. 

With the FHA program alternative credit can be used.  But many lenders will not consider the rent as a "line of credit" since you are the landlord and I am not sure if they have any car insurance, cell phone bills or any other monthly obligations that will help establish credit.

As mentioned in the other post, your parents will need to show 24 months of stable employment, so they are close to 2 years out before buying.  That gives them plenty of time to establish credit and income stability.  They should establish at least 3 active "trade lines" (if need be they can apply for a gas card and secured credit card with small limits, just pay them off every month) for a minimum 12 month history.

Find a knowledgable loan officer in your area who is willing to work with your parents and monitor their progress every 6 months to make sure they are moving in the right direction.