What ingredient, besides beans, creates a complete protein together with rice?
Rice tends to be high in the sulfur-containing amino acids, cysteine and methionine, but low in lysine.  So want you need to complement the rice are foods high in lysine.  Remember that the average adult male only needs about 3g of lysine daily which is easily provided by 3-4oz (90-120g) of meat, eggs, dairy, or soy protein (tofu, tempeh, lufu, miso, etc).  Since you do eat meat, all you need to do to save money and still get a complete protein is to eat less.  If you need more bulk in your meals, include a variety of vegetables, or a salad topped with nuts or seeds.

People who eat meat and other animal products to meet their recommended protein intake don't need to worry about not getting enough of any individual amino acid. Even vegetarians usually don't have a problem with this as long as they eat a variety of different plant-based protein sources, since beans with grains, beans with nuts or seeds and grains with nuts or seeds are all combinations that provide enough of all of the essential amino acids.

Also, it is not necessary to take in the full complement of essential amino acids in one sitting, as long as you eat at least the minimum required amounts over a 24 hour period.