How to make a kid's bike easier to pedal My daughter has a hand-me-down 16" wheel bike, and she finds the pedals very difficult to turn. The bike currently has a single-speed coaster hub on the back. Is there any way to replace the rear hub/wheel with something that has an easier gearing? 

I'm aware this could cost more than the bike is worth, but other kid's bikes seem to share this problem. Could it be an issue with chain tension, or are there other ways I could fix this?
Children's bikes are usually designed with easy gearing appropriate to children.
As Chris H said - they are not usually assembled by people who care that a bike is assembled correctly. From the factory it seems like everything is always too tight.

My guess is that there is something that can be adjusted to make things better.
Flip the bike over so it's sitting on it's seat and handlebars.
Pedal the bike and see how it feels. This will give you a baseline to know if you've made improvements as you adjust things.

Things that make a bike hard to pedal:


You are right to ask about chain tension. If the chain is tight it will be hard to pedal. You may be able to loosen the chain a little and feel an improvement immediately.
Rear wheel hub adjustment. With the brake disengaged the wheel should spin freely. If it does not you'll need to loosen the bearings on the hub.
Crank bearings. If the chain tension is OK slip the chain off the chain ring and feel how easy the crank is to move. If the crank is stiff you'll need to loosen the crank bearings.


Edit:
Adjusting Chain Tension
(When I started writing this I thought it would be a few steps - but it kept getting longer...)

There is the easier way and the slightly harder way to adjust chain tension.  

The Easy Way


Remove the nut on the chain side of the wheel that holds the training wheel.
With the training wheel off loosen the nut that holds the wheel on.
At this point you may be able to squeeze the chain and get a little slack in the chain . Since you are only shifting one side of the wheel adjusting this way can put the wheel off center in the frame. That's OK as long as the tire does not rub on the frame. If you are able to get enough slack in the chain to smooth out pedaling without having a tire rubbing on the frame you are done - go to step 4.
If the tire is rubbing skip step 4 and to "The Slightly Harder Way" step 1.
Note: if you wanted to tighten the chain pull the right side (right side of the wheel looking at the wheel from the chain side) of the wheel toward you.
Re-assemble in reverse order.


If the tire is too far off center
The Slightly Harder Way (continuing from the previous steps)


Get the chain tension where you want it and tighten the nut that holds the wheel. This will set your chain tension.
Remove the nut that holds the training wheel on the non-chain side.
With the training wheel off loosen the nut that holds the wheel.
At this point you may be able to center the wheel and re-tighten the nut. If the wheel won't center - step 5



Picture of the non-chain side and the brake strap after the training wheel is removed.
 1. Loosen the screw that holds the brake strap (you may need a wrench to hold the nut on the other side of the screw).
 2. Center the wheel
 3. Tighten the nut that holds the wheel
 4. Tighten the screw that holds the brake strap
 5. Put the training wheels back on