Since we're talking about calculations...
You have a 1000 gallons of water. That's a good round figure to use.
Since one gallon of seawater weighs somewhere between 8.34 and 8.54 lbs per gallon, you have an estimated 8,340 lbs of water in your system.
To cool that much water just one degree and keep it at that temperature, you need 8,340 BTU/h of cooling capacity. No residential fridge or freezer is that powerful. They are rated in hundreds of BTUs, not thousands.
Keep in mind, you aren't cooling air, you're cooling water. Water takes a tremendous amount of energy to cool, cubic foot for cubic foot, compared to air.
You didn't mention to me how much you need the water cooled, but if you are looking at a even a two degree cooldown, you need a massive amount of cooling... 16,680BTU/h, etc.
I am a firm believer that almost everything can be built by someone with the guts to try it, but chillers are one of those things that make me say "almost."
If I was really intent on DIYing this, then I'd be using a really big window AC unit... maybe 12,000-18,000 BTU or so.