How can I fill a wheelbarrow tire when the bead is gapped away from the rim?
Looks like the typical gap one gets when mounting a tubeless tire.  You'll need to get the bead to seat against the rim as you pump air (hopefully quickly) into the tire - a hand pump might not do it.  

Sometimes you can jiggle the tire to effect a temporary seal around the bead as your compressor dumps air in.  Using a clip-on tire chuck will help.

Some folks "squeeze" the tire with a strap around the tread area.  I've seen a device called a bead expander, and this guy shows the use of some large tie-wraps to achieve the same thing.