While you can do things with good manners, it is rare to direct someone to do so in imperatives.
Unless addressing children, it is not required to remind people to be polite— a person with good upbringing has good manners out of habit; an poorly raised person cannot tell the difference, anyway.
This may reflect a difference of cultural perception, but I think more likely that it is simply a poor translation from Japanese.
A search on "smoke with good manners" mostly returns results from Japan.
Considerate would be the more idiomatic adjective to use to remind people to think of others, so a similar campaign in an English-speaking city might be
please be a considerate smoker or please be considerate when smoking , phrasings which are common in such signs.
When speaking generally of politeness, consideration, and other positive social behavior, good manners are something you have , not something you do (as with one's habits or one's nature ).
Someone with good manners may be said to be well-mannered , and someone without good manners is ill-mannered ; it is more usually expressed that someone has good manners, than that they do something with good manners.
ell.stackexchange.com/users/21/choster
In Japan, there are many odd (and sometimes unintentionally hilarious) signs with translations of Japanese phrases into English.
This is a good example, as "please smoke with good manners" is not at all idiomatic.
A more idiomatic version might be:
Please be considerate of others when smoking in the area surrounded by planters.
or Please be courteous when smoking in the area surrounded by planters.
Side note:
One of the funniest "Japlish" signs I ever saw was from a train station, which advised passengers: Please do not run into the train.
Good advice to be sure, but more likely they meant to say Please to not run onto the train.
/
Please do not run to get on board the train Logically, "into" makes sense, but unfortunately the phrasal verb "run into" something means "collide with", usually "head-on".
I suspect most people know it's not a good idea to run into trains.
(Edit)
For general interest: A direct translation from the Japanese マナーを守って (mana o mamotte) would be:
Please mind your manners
when ...
However this is somewhat too strong for a public sign, as it's the kind of thing parents might say their children, or a teacher to her students.
Now children, be sure to mind your manners when we are at the museum, otherwise they won't allow us to come back.
A more nuanced translation would be "be courteous".
ell.stackexchange.com/users/42184/Andrew
It is not uncommon to see "with good manners".
For example see Google and Google Books .
You can learn good manners, practice good manners, or keep good manners.
ell.stackexchange.com/users/61125/Eddie Kal
A Japanese speaker might offer a better phrased translation, but this doesn’t seem too bad.
One can use good manners in other actions.
A smoker can be mindful of those nearby and carefully dispose of the remains.
That would seem to be good manners.
As others noted, “be considerate” would be how one would word this in English, typically.
ell.stackexchange.com/users/516/JTP - Apologise to Monica
A native Japanese.
We are so embarrassed that our English literacy is so low despite the mandatory English study span
is 6 years in the shortest.
For example, a guidance of a community bus of one of the wealthiest district of a prefecture says, Abide by Low .
O.K.
How can we abide by Low , man!
Correct it to Law right now!
But towards 2020 Tokyo Olympic, the English guidance or announcements are getting improved gradually, but especially in rural areas, there are still many signs with strange English.
For example, Please notify the train crews if you find unclaimed and suspicious objects or persons
Okay, so if I find someone whose behavior seems to be strange, am I obliged to call the crews?
F::k
my country's English.
Hahahaha, An another odd guidance from one of the wealthiest districts.
(Many native English speakers live here.)
PLEASE STAND AT SEAT AFTER STOPPING.
So do we need to stand up at the seat every time bus stops?
Did the guidance try to mean "Please stand up from your seat after the bus stops"?
Oh..my lovely country always full of harmless and innocent but stupid instruction everywhere lol.
(Found today)Did the guidance try to mean "Please stand up from your seat after the bus stops"?
Oh..my lovely country always full of harmless and innocent but stupid instruction everywhere lol.
(Found today) Hahaha, here is an another shot from a Tokyo metropolitan subway.
As the Tokyo Olmpic gets closer, the "announcement" in English is getting improved in rapid pace.
But the banner of the central Tokyo subway is still behind the schedule?
Even though it looks they are appointing the "professional" English speakers?
Enjoy Tokyo with Good Manners!
ell.stackexchange.com/users/17814/Kentaro
Alternatively, keeping "manners" in the title, it could be phrased as: Practice good manners while smoking in the area surrounded by planters.
Although "courteous" is what they're trying for with that translation, it is understandable.
ell.stackexchange.com/users/94766/SentientFlesh
In Tokyo, I saw this sign next to the smoking area.    It says   Please smoke  with good manners  in the area surrounded by planters.   The part "with good manners" sounds a bit weird to me. Is it just me, or is it not idiomatic?  One can have/teach/forget manners   He dressed well and  had  impeccable manners.  They  taught  him his manners.  I'm sorry, I  was forgetting  my manners.   but "with manners" seems a bit off, doesn't it? How would you say it?
Please, smoke with good manners
ell.stackexchange.com
<phrase-meaning><phrase-choice><idiomatic-language>
ell.stackexchange.com/questions/208374
ell.stackexchange.com/users/53961/Andrew Tobilko
When speaking generally of politeness, consideration, and other positive social behavior, good manners are something you  have , not something you  do  (as with one's  habits  or one's  nature ). This may reflect a difference of cultural perception, but I think more likely that it is simply a poor translation from Japanese. This is a poor translation from Japanese and while it is not uncommon to see "with good manners" the use of "courteous" would be more appropriate. 
This is a poor translation from Japanese and while it is not uncommon to see "with good manners" the use of "courteous" would be more appropriate. 