Dining plans are available with only two types of reservations: 1) package reservations made through Walt Disney Travel Company, and 2) reservations made by Disney Vacation Club members through DVC Member Services. Without one of these two types of reservation, there's no way to get a dining plan.
You would have to forego any discounted convention rooms if you want a dining plan. These are sold solely as room-only reservations, not packages, and most of the time they're booked through the convention itself, not through Disney.
You could book yourself and your party a package reservation if you want the dining plan badly enough to cancel your convention discounted room. If a discount on packages is being offered at the time you travel, you could get that discount. Unless you are an annual passholder or qualify for the military room discount, however, you will have to purchase at least a one-day theme park ticket for everyone in your room to make your reservation a package and qualify for the dining plan. You would have to contact WDTC to do the booking, not go through the convention.
You could also rent points from a DVC member. The DVC member could then book a reservation for you through Member Services, and add a
Disney Dining Plan. You would then need to pay the member for both the reservation and the dining plan. No ticket purchase would be required.