Buying a Lawn Sprinkler That Will Water a Narrow Strip

Look for "soaker hose", which is porous, round hose. If you only turn your faucet on partially, it weeps; if you turn more pressure on, it will spritz. If you experiment with the pressure, you should be able to get your grass strip nicely. The other alternative, would be to get a few five gallon buckets, drill holes in the sides at the bottom, and put them on the strip, fill with the hose, and let them water the strip.