You will need work thewith an interval slider in terms of AbsoluteTime
values because the slidersuch sliders only workswork with numeric objects. Here is a demonstration where a interval slider has the behavior you want.
With[{
min0 = AbsoluteTime @ DateObject[{2015, 3, 8, 10, 0, 0.}],
max0 = AbsoluteTime @ DateObject[{2015, 3, 8, 12, 30, 0.}],
minT = AbsoluteTime @ DateObject[{2015, 3, 8, 0, 0, 0.}],
maxT = AbsoluteTime @ DateObject[{2015, 3, 8, 22, 30, 0.}]},
Manipulate[
DateString /@ span,
{{span, {min0, max0}, "Interval"}, minT, maxT, 5 60,
ControlType -> IntervalSlider}]]