First: A request is just that....a request. There is no sure way of getting it, otherwise it would be a guarantee.
Second: All Disney resorts require you to PAY an additional fee per night for a King bed.
Example: At moderates a Standard Room ranges from $149 - 219/night, a Waterview ranges from $174 - 249/night and a King bed ranges from $174 - 249/night depending on what "season" you stay during.
Otherwise bedding is as follows:
Value: 2 doubles (standard or preferred)
Moderate: 2 doubles expect Coronado Springs which is 2 queens (standard or waterview) or 1 King (additional $$)
Deluxe: 2 queens (standard/garden/water/club level etc.) or 1 King (additional $$)
You cannot "request" a King bed unless you are willing to pay extra for it.
For room requests, you can have Disney Reservations note it on your reservation and you can fax the resort 4 days prior, but once again, there are no guarantees that any requests will be granted.