If you're using power saves you have to convert them to the correct format first. (ie if the save you downloaded is .wii it must be converted to .bin to work on the wii). Otherwise you would datel's power save sd card. I beleive if you search through the apps in gba temp you'll find the tool to convert power saves to normal saves.
If it's in the normal .bin it should work as long as you have the save in the proper folder sequence. (ie: it's in the private/wii/title/xxxx folder where xxxx is the game's id code.) If you're unsure of the game's id save the game then transfer that save to your sd card now load the sd card on your pc and replace the saved file the wii created with the one you downloaded.
Hopefully one of those two tips helps you out a bit.