In magento shopping website, My admin settings are:
Allowed countries : United Arab Emirates.
Enabled Shipping methods are.
flat Rate : 10 AED
Free Shipping
Its working fine when i disable onepage checkout option..
When i enable onepage checkout it showing Sorry, no quotes are available for this order at this time
.. Only when i enable onepage checkout option.
Essentially this statement refers to Magento not having a shipping method for address entered or your config caches are stale and don't have this setting saved.
Please try entering an address for United Arab Emirates in one page checkout and after you flush all of your caches try again.