Is it possible to create a shaded error region for a scatter plot?

The basic answer would be: there is no easy way to do so.


Now one simple proposition
Especially suited to case when you have hundreds of points heavily clustered with no or few outliers.
Draw error bars, but with light gray lines, no ends, and noticeable thickness (12 points was used in attached file)

And suggestion for second approach (more effort would be required) create additional set of points and draw it as light gray markers

for each x; y point prepare 4 points: x-xerr; y-yerr x+xerr; y-yerr x-xerr; y+yerr x+xerr; y+yerr
or may be also four more, like x-xerr; y x+xerr; y x; y-yerr x; y+yerr

Then the cloud of these extra points drawn with light gray could well simulate shaded region

And some remarks:

To give more precise answer the question shall be also more precise or goive more details:
how many points? (too many is not precise enough, for one it could be 20 for someone else 2000 or more)
how many series?
are errors constant for all points, or calculated, or are they defined for each point separately?
are there both horizontal and vertical error bars?
are scales verical and horizontal similar (like both in range 0-10) or different (say one 0-10, another one 100-500)?
...

And additional comments:
- what do you mean declaring version 10 in your profile? Are you using excel 2010 or may be Windows 10 and Office 365? The excel changes over years and new tools are added.
- the question is on general forum, but have you noticed we do have separete section of forum on: https://www.excelforum.com/excel-charting-and-pivots/