There are a number of things that will help, but your koi may be to young yet. Typically, the koi need to be in their third or fourth year before they are sexually mature enough to spawn. Factors that affect spawning of mature fish are time of year, phase of moon, and lots of fresh water. They typically spawn just once a year, so it happens in the spring when the water temperatures are rising, for those in the northern hemisphere, late April, to mid July would be most likely, so I think based on that you are past the breeding season this year. I usually found spawning happening with the full moon. A major water change gives them a nice clean bed and they have to mess it up. I have seen koi release eggs at shows where they are put into all new water.
When they do spawn, you will find the pond smells of sex, and has a lot of foam on the surface. The older koi will gorge themselves on the eggs, eating as many as possible. The milt is high protein, the eggs are high protein, and the high activity of the fish consumes a lot of protein, and the protein becomes ammonia, which becomes nitrites, both of which are toxic, so major cleanup is highly advised. I have vacuumed the eggs from the pond and either moved them to another hatching tank or destroyed them to prevent as much as possible the damage to the water quality. I have raised several batches of fry and gotten lots of culls and only one or two keepers. Not worth the trouble, but I guess we all have to do it at least once.
Zone 7 A/B
Keep your words sweet. You never know when you may have to eat them.
Richard