My girlfriend's parents will be in town and I will meet with them for the first time and I'm plannig to propose her right before they get here.
Is there some manner for me to know about Japanese parents?
I think it's the same as how the Americans do.
Once you meet her parents, you formally have sit them down and tell her father that you would like take her as your wife. And, he'll reply by saying yes take care of her, or no way.
In our case, my parents don't really speak English, so I told my parents that we are getting married, and after the grilling questions like "do you own a property", "what's your retirement plan", "where do your parents live", "how much do you make a year", "how much was your bonus last year", etc., there was an OK. My father is a "straight to the point" kind of a guy , and kept saying "you do not need to impress me so do not lie".
As a recently engaged Japanese woman to an American guy, my best advice is that make it clear that you genuinely love her and be honest about yourself with her parents.
I hope this helps.
Good luck sunny!
Do not kiss her in front of her parents, they'll think your are a perv.
When my husband first met my parents before we got married, he told my parents "Watashi wa Yume-chan wo makes NO1! happy!"very mixed poor Japanese, but he made my mom laugh and my dad said "he looks so sincere".
Don't worry, sunny.
Show her parents your love and how you care about her and her parents toward your girlfriend.
B-kyu Gourmet 
