Scurvy was a problem for sailors worldwide, but there's a distinct focus on Western practices due to my location. So before people learned about the importance of Vitamin C, what did sailors and nations try to use in places such as the Middle East, Africa, and Asia?
I think a better question might be to ask if there were any recorded attempts made as a national concern in the Middle East, Africa and Asia to cure scurvy? (I'm not aware of any, but then I'm not aware of any medical or sailing texts from those nations that discuss the issue.)
When considering pre-cure scurvy theories, you have to ask two questions:
Unfortunately for your original question, the answer to both is Europe. Most long voyages were undertaken by nations like France, the Netherlands, England, Portugal and Spain. Most of the medical advances were during this time were coming from similar places. Thus most of the theories on how to cure scurvy were European.
I am not saying there weren't any non-European cures for scurvy - in fact there probably were. I am saying that if such theories existed, they aren't as well known because they are less likely to have been recorded and published. Since scurvy as a widespread, national problem mostly affected the European nations, the recorded attempts to cure scurvy are mostly European.
(For an interesting account of how the cure for scurvy came about, including how it was discovered in the 16th c. and then sort of lost again in the 17th, see Stephen R. Bown's book Scurvy: How a Surgeon, A Mariner and a Gentleman Solved the Greatest Medical Mystery of the Age of Sail.)