Use FrameTicks -> {{left, right},{bottom, up}}
DateListPlot[data, FrameTicks -> {{{{0.0, "0%"}, {0.1, "10%"}, {0.2, "20%"}, {0.3, "30%"}, {0.4, "40%"}, {0.5, "50%"}, {0.6, "60%"}}, None}, {Automatic, None}}]

A table for FrameTicks
can be generated, for example,
Table[{k/10., ToString@ (10 k) <> "%"}, {k, 6}] (* Out[10] := {{0.1, "10%"}, {0.2, "20%"}, {0.3, "30%"}, {0.4, "40%"}, {0.5, "50%"}, {0.6, "60%"}} *)
If you need to make a lot of numbers, LevelScheme is a free package that makes it easy to create good sections in Mathematica, especially when it comes to grades.
EDIT: As suggested by Jagra, there is a function here that makes a list of tick specifications based on a dataset and with desired tick steps. The assumption is that the data structure is always the same.
ticks[step_, data_] := {{Table[{k, ToString@IntegerPart @(100 k) <> "%"}, {k, Floor[ Min@data [[All, 2]], step], Ceiling[ Max@data [[All, 2]], step], step}], None}, {Automatic, None}};
Now you can define the plotting function
plot = DateListPlot[
and use it like this: plot@data
Finally, since any Mathematica graph indicates your question, remember that FrameTicks
only works on frame graphs, for other graphs use Ticks -> {{x ticks},{y ticks}}
.