Job Sharing Elder Position?

The Church Order is really remarkably silent on the question you
raise. The number of elders required in a given church is really left
to the judgment of the consistory and council. The only functioning
principle is that the needs of the congregation must be met. In other
words, there should be a sufficient number of elders so that the
pastoral care "gets done." Family visiting once a year is another
goal in the Church Order, of course, and many churches can't even
manage that -- so they find other solutions. It still seems like a
laudable goal to me as long as elders can also be creative about it --
have lunch with somebody instead of insisting on meeting at their
home, for example. If indeed you are truly feeling that more folks
are needed to do the work of the elders properly, perhaps you should
increase the number of officebearers. Another possibility is to
reduce every district by a half -- if, indeed, you still work with
districts. In that case it's not really an issue of "job sharing" but
of being more realistic about how many folks are assigned to one
pastoral elder.

The only consequence of involving more people is that they really
should all be ordained and that ordination gives them the right to be
a member of the council and of the consistory. I don't know whether
you have administrative elders and pastoral elders distinguished in
your church, so I also don't know precisely how you configure the
council and the consistory. But the principle in the Reformed
tradition is definitely that anyone functioning as an elder should be
ordained. The only thing I've seen in other churches that departs
from that principle is to have, in addition to the elders, so called
associate elders or elders' assistants. They are people who are not
ordained but "commissioned" to their task and they do much of the
routine visiting under the guidance and supervision of the elders.
This might include visiting the shut-ins and elderly, having lunch
with young people, even joining an elder at a more traditional home
visit, and looking after birthday wishes, well-wishes for the sick,
return visits for the bereaved, etc. In that case people are not
officially ordained and therefore do not have a right to be seated at
the council or consistory table.

Much of this, in other words, is left to the discretion of the local
church and not regulated by the Church Order.

I agree with Henry. The position of elder is one the includes ordination. Anyone serving in the capacity and/or function of elder needs to ordained into the position.
What other "work" do your elders do? If any of the tasks your elders perform do not require an elder than that might be one way of lightening the load. For example, we have an elder sit on each of the four main committees to act as a council liaison. While this does mean one more meeting per month, that elder is not to serve as the chair person of that committee.

My church has had married couples sharing an elder role. They're both full-fledged elders, but only one attends elder meetings at a time (i.e. one vote).

It's been a real blessing - both for their district who benefits from the gifts of two people, and for the couple as they work side-by-side in ministry. Win win, in my opinion.

Last month, we installed a married couple as deacons for the first time. I expect it will be as positive an experience as we've had with couple elders.

While official elders should be ordained, scripture seems to indicate that many people can be pastors, or pastoral in terms of relating to fellow christians.   This means that others besides elders and deacons can visit the sick, assist the needy, teach, provide pastoral advice in stressful situations, etc.  And while all elders should be apt to teach, it is not necessary for all teachers to be elders.  So some teaching jobs can be done by non-elders. 

 It would also be possible if a serving elder is overwhelmed at times by people who need attention due to illness, stressful family situations, job loss, etc., that he could ask for assistance from non-serving or "retired" elders.   If these "retired" or "off-duty" elders took their initial calling seriously, then they wouldn't mind helping out if they have the capacity, time  and ability.