It is not possible to specify individual individual effects for the next and previous buttons without changing the source code of the plug-in.
Closest you can specify several effects in the fx options. They will be used sequentially. Example:
$('#slideDiv').cycle({
fx: 'fade,scrollHorz',
prev: '#prev1',
next: '#next1',
timeout: 0
});
, , next prev, "fade", , , "scrollHorz", "fade" ..