the certificate of marriage is the certificate of accepting (by city office) the application (by you) of your marriage registration at that time. it does not prove your marriage is still continuing. they request you are currently married and are living together.
you don't have your koseki. your name is there in her koseki. take her koseki-tohon, i.e. zenbu-jikou-shoumei.
you have your own jyuminhyo, jyumin-toroku.
you should get a family record of jyuminhyo. it have your name and your wife's name in one sheet.(you have to have that one).
if you get her jyuminhyo, it might contain her name only.
make sure that you and your name should be there together in both documents.
a guarantor is a person who guarantee YOU(not your marriage). that person must be closest. therefore, your wife !
it is essential the certificate of your wife's income, certified by city office.
get nouzei-shoumeisho or shotoku-shoumei, something like that at the city office. the document should have information about her total income and the tax amount she payed.
that should be the 2013's income, if she take now. she may add a photocopy of gensen-choushu-hyo of 2014 to prove 2014 income.(then it seems perfect.)
I think a copy of the contract is unnecessary. they only want to know she has income enough for your living.
if her income is not enough, then they ask you the certificate of your income.(if they ask your income certificate, you get your nouzei-shoumei at city office. the contract is not sufficient to prove your income.) they request the certificates which are issued by governmental offices (city office).
all the documents obtained from city office should be issued within 3 months before your application.(the documents are only valid for 3 months.)
the detailed explanation is here in Japanese.
your wife can easily understand what they request.
http://www.moj.go.jp/ONLINE/IMMIGRATION/ZAIRYU_HENKO/zairyu_henko1.htm...the point uncertain is:
in the official website, they request the marriage certificate from your country, although AK says not necessary.
4 申請人の国籍国(外国)の機関から発行された結婚証明書 1通