Is it a show corona???or a 4 x 4 corona??? if not then id suggest stick to 15' max...they are cheaper for tyres and heaps easier to get second hand etc.
There won't be any problems fitting a set of 16's provided you get suitably low profile tyres to keep the overall diameter the same as original. The offset should be the same as (or similar to) the original wheels; not sure what that is though.