Hey @Ryan Beetham
Based on your criteria, I think the best you can case scenario is finding something where the numbers are better than renting. Trying to cash flow with $0 down on a $1M-$2M property is going to be very tough here. Also, trying to do it with a property that doesn't need a fair amount of work.
Assuming you're at Schofield or Shafter, the best options for neighborhoods are Waialua, Mililani, Moanalua, Kaneohe, and Kailua. These are great neighborhoods, but if there are any multi units, it will likely be two units. Meaning you can expect about $1500-$2000 a month in rent (assuming your family lives in the bigger of the two units).
Appreciation here is good, but if you're here for three years (maybe 2.5 now) you can expect the appreciation gains to cover closing costs, essentially breaking even. If you're here longer than three years, then there's a good chance of coming out ahead.
There isn't a whole lot of variety in property types on Oahu, especially in good neighborhoods. So you've probably seen every property type available. There are off market opportunities, but not anything (property types) you haven't already seen. Some could come at a discount, but a fair amount of remodel work will be needed.
If you're looking for a solid long term investment, some criteria may need to be adjusted. For example property condition and neighborhood, but these can be tough when you have a busy job and family needs.
If you're okay with something that beats renting, then that is definitely doable.
Feel free to reach out with additional questions or for further discussion.
Aloha! Isi