Try this Link.

http://www.gov.qa/wps/portal?New_WCM_Context=/wps/wcm/connect/cnt/en/1_h...

You should be able to get a Qatar Airways visa which is valid for 2 weeks. This can be renewed for 2 more weeks max (28 Days in total). Pl visit the exit permite office which is located just outside the airport. This is where you need to apply. If they are over 60 you may need the approval from teh captain who will be available in the morning. This office is open 24Hrs. You can go and give a try at the counter. The form is very simple to fill. Just ask for the QR Visa form. If they accept you will be given a receipt and you can print the visa from internet. VISA will normally be ready in 3-4 hours.You have to go with your Bank Debit card as they dont accept cash for payments.

Hope this helps a bit.