I have never hacked Gecko conditionals, so I have no idea how that works.
If the existing Gecko version doesn't work when entering it in the Gecko Codes section, you can hack the AR equivalent of the conditional using the built in cheat search of Dolphin (there are many other methods too, such as Cheat Engine).
The condition value varies depending on your control scheme, but assuming you are using Wiimote+Nunchuck: http://geckocodes.org/index.php?arsenal=2 you can easily find the address.
By enabling background input you can have the Cheat Search window active while doing a 16-bit search on the value you are holding down buttons for (0x6000 if holding Z+C, 0x2000 if only holding Z and so on), just keep searching Equal and swapping between any given combination, and not holding any buttons down (0x0000).
Once you've narrowed it down to the last few addresses, and they don't seem to disappear anymore, you make an AR conditional with the addresses you've found and the button combination you want to use for activation (0Axxxxxx 0000yyyy) testing each of them until you find the one working.
This is not guaranteed to work for every game but in many cases it is enough to find it.
The same goes here, you can't use the AR conditional in the Gecko section, so the code you want to activate must also work when entered in the AR section.
The values you see at the bottom of the GC AR codetypes document do not apply to Wii games. You will need the same values as Gecko uses.
Edit: As an example I used the above method to aquire the AR conditional for Resident Evil 4 Wii [NTSC-U], and these are the conditionals for AR and Gecko respectively:
AR
0A344C9C 00006008 (C+Z+Up on dpad)
Gecko
2832FF1A 9FF76008 (C+Z+Up on dpad)
As you can see, they are not very similiar other than the 6008 part, which is C+Z+Up. 9FF7 is 6008 in reverse, but I'm not entirely sure what function it has. As far as AR conditionals go I think you can disregard that and go with 16-bit.
Edit2: Btw, when you tried the button activators for FE:RD did you try
Wii Remote All Buttons Address [g6flavor]
283D78DA 0000xxxx
your code(s) here
E0000000 80008000
or one of the
Button Activator for Gamecube Controller(Hold ?) [ShadowX39]
283D78AE 0000xxxx
?
The one for GC controller will never work as Dolphin doesn't emulate that on Wii games. If you haven't already, you can try the Wii Remote one, and remember to enter it in the Gecko tab. If you have the offsets or if the codes already work from the Gecko tab this activator should also work, in which case you would not need to hack the AR conditional.
If the existing Gecko version doesn't work when entering it in the Gecko Codes section, you can hack the AR equivalent of the conditional using the built in cheat search of Dolphin (there are many other methods too, such as Cheat Engine).
The condition value varies depending on your control scheme, but assuming you are using Wiimote+Nunchuck: http://geckocodes.org/index.php?arsenal=2 you can easily find the address.
By enabling background input you can have the Cheat Search window active while doing a 16-bit search on the value you are holding down buttons for (0x6000 if holding Z+C, 0x2000 if only holding Z and so on), just keep searching Equal and swapping between any given combination, and not holding any buttons down (0x0000).
Once you've narrowed it down to the last few addresses, and they don't seem to disappear anymore, you make an AR conditional with the addresses you've found and the button combination you want to use for activation (0Axxxxxx 0000yyyy) testing each of them until you find the one working.
This is not guaranteed to work for every game but in many cases it is enough to find it.
The same goes here, you can't use the AR conditional in the Gecko section, so the code you want to activate must also work when entered in the AR section.
Edit: As an example I used the above method to aquire the AR conditional for Resident Evil 4 Wii [NTSC-U], and these are the conditionals for AR and Gecko respectively:
AR
0A344C9C 00006008 (C+Z+Up on dpad)
Gecko
2832FF1A 9FF76008 (C+Z+Up on dpad)
As you can see, they are not very similiar other than the 6008 part, which is C+Z+Up. 9FF7 is 6008 in reverse, but I'm not entirely sure what function it has. As far as AR conditionals go I think you can disregard that and go with 16-bit.
Edit2: Btw, when you tried the button activators for FE:RD did you try
Wii Remote All Buttons Address [g6flavor]
283D78DA 0000xxxx
your code(s) here
E0000000 80008000
or one of the
Button Activator for Gamecube Controller(Hold ?) [ShadowX39]
283D78AE 0000xxxx
?