C-up and C-down are bound to org-timestamp-up and org-timestamp-down. These methods use the variable org-time-stamp-rounding-minutes:

Number of minutes to round time stamps to.

These are two values, the first applies when first creating a time stamp.

The second applies when changing it with the commands ‘S-up’ and ‘S-down’.

When changing the time stamp, this means that it will change in steps of N minutes, as given by the second value.

So we can change the second value to 30:

(setf (elt org-time-stamp-rounding-minutes 1)
      30)

And now these methods will move by 30 minutes^1.

[1] It will move to the nearest multiple of this value; C-up once on <2019-10-09 Wed 06:27> will move it to <2019-10-09 Wed 06:30>; calling it again gives <2019-10-09 Wed 07:00>.

S-up and S-down are bound to org-shiftup and org-shiftdown. On timestamps, these call org-timestamp-up and org-timestamp-down respectively. These methods use the variable org-time-stamp-rounding-minutes:

Number of minutes to round time stamps to.

These are two values, the first applies when first creating a time stamp.

The second applies when changing it with the commands ‘S-up’ and ‘S-down’.

When changing the time stamp, this means that it will change in steps of N minutes, as given by the second value.

So we can change the second value to 30:

(setf (elt org-time-stamp-rounding-minutes 1)
      30)

And now these methods will move by 30 minutes[1].

[1] It will move to the nearest multiple of this value; S-up once on <2019-10-09 Wed 06:27> will move it to <2019-10-09 Wed 06:30>; calling it again gives <2019-10-09 Wed 07:00>.