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##Ruby 1.9, 85 characters

f=->a{require"date";d=Date.parse(a,0,0)+1;d+=1until d.day*d.month==58;d.strftime"%A"}

Straightforward solution. Call the function with f[args].

• Edit: (87 -> 97) Fixed the 0001年01月01日 testcase.
• Edit 2: (97 -> 91) Date.parse allows specifying the date of the calendar reform as well.
• Edit 3: (91 -> 87) Use a lambda instead of a function. Thanks Dogbert!
• Edit 4: (87 -> 85) Remove unnecessary spaces. Thanks again, Dogbert!

Ruby 1.9, 85 characters

f=->a{require"date";d=Date.parse(a,0,0)+1;d+=1until d.day*d.month==58;d.strftime"%A"}

Straightforward solution. Call the function with f[args].

• Edit: (87 -> 97) Fixed the 0001年01月01日 testcase.
• Edit 2: (97 -> 91) Date.parse allows specifying the date of the calendar reform as well.
• Edit 3: (91 -> 87) Use a lambda instead of a function. Thanks Dogbert!
• Edit 4: (87 -> 85) Remove unnecessary spaces. Thanks again, Dogbert!

##Ruby 1.9, 85 characters

f=->a{require"date";d=Date.parse(a,0,0)+1;d+=1until d.day*d.month==58;d.strftime"%A"}

Straightforward solution. Call the function with f[args].

• Edit: (87 -> 97) Fixed the 0001年01月01日 testcase.
• Edit 2: (97 -> 91) Date.parse allows specifying the date of the calendar reform as well.
• Edit 3: (91 -> 87) Use a lambda instead of a function. Thanks Dogbert!
• Edit 4: (87 -> 85) Remove unnecessary spaces. Thanks again, Dogbert!

##Ruby 1.9, 85 characters

f=->a{require"date";d=Date.parse(a,0,0)+1;d+=1until d.day*d.month==58;d.strftime"%A"}

Straightforward solution. Call the function with f[args].

• Edit: (87 -> 97) Fixed the 0001年01月01日 testcase.
• Edit 2: (97 -> 91) Date.parse allows specifying the date of the calendar reform as well.
• Edit 3: (91 -> 87) Use a lambda instead of a function. Thanks Dogbert!
• Edit 4: (87 -> 85) Remove unnecessary spaces. Thanks again, Dogbert!

##Ruby 1.9, 87 characters

f=->a{require"date";d=Date.parse(a,0,0)+1;d+=1 until d.day*d.month==58;d.strftime "%A"}

Straightforward solution. Call the function with f[args].

• Edit: (87 -> 97) Fixed the 0001年01月01日 testcase.
• Edit 2: (97 -> 91) Date.parse allows specifying the date of the calendar reform as well.
• Edit 3: (91 -> 87) Use a lambda instead of a function.

##Ruby 1.9, 85 characters

f=->a{require"date";d=Date.parse(a,0,0)+1;d+=1until d.day*d.month==58;d.strftime"%A"}

Straightforward solution. Call the function with f[args].

• Edit: (87 -> 97) Fixed the 0001年01月01日 testcase.
• Edit 2: (97 -> 91) Date.parse allows specifying the date of the calendar reform as well.
• Edit 3: (91 -> 87) Use a lambda instead of a function. Thanks Dogbert !
• Edit 4: (87 -> 85) Remove unnecessary spaces. Thanks again, Dogbert !