Who pays for the water bill? If its your neighbors, great idea. Good idea to use a splitter at the faucet location. Check your water pressure with a gauge at the faucet. You should have enough pressure to reach up 15 feet to your garden if the faucet pressure is 50-60 psi. I would run 1/2" pvc line (hard line) to your garden following the stairs as invisibly as possible and the paint it to match the stairs. Create a hose bib/fuacet on the deck at the garden level then use a hose or removable drip lines from there. Be careful of leaving the system on by mistake or the lines blow out unless you are the one living below your garden. You probably will be using a pressure reducer with the drip system. aloha

Thank you! What about using a rain barrel (that I would fill periodically with a hose) on my deck and running irrigation through that? I will probably only have a handful of planters, so I would hope that the water pressure would be adequate if I elevated the rain barrel up on a stool.

If you can elevate the rain barrel 6 feet above the dripper you will have 2.5 psi and the pressure will drop as the water level goes down. Most drip systems are in a range of 10 to 30 psi. With 2.5 psi you may get a few drops but it will be inconsistent.

You won't be able to use standard drip designs. You may have to just use 1/4 line with no dripper attached.

I would not recommend a barrel of water on your deck. This is because your deck may not be able to carry the weight. A barrel of water is very heavy (liability). These barrels are usually support by the ground or racks on the ground. And as the previous writer said you don't get much pressure. There are low-pressure drip systems but they are pvc pipe drip lines not drip tape. I can explain those if you are interested. I don't think an automated system would do well because if unattended significant water damage could occur. You need to check your plants every time you water to check for plant health, diseases and insect damage anyway (Zen part of gardening). Didn't anyone tell you that is the fun part of gardening. aloha

I have done similar installations for balcony planters/pots, however I used 3/4" poly pipe to get the water there, instead of PVC because the poly is more UV resistant. poly is also more flexible, and may sag depending on how you plan to run it up under the stairs. PVC will gain substantial UV protection if painted as Lehua suggested. from there you could run right into 1/4" drip tubes.

you could also install a reliable timer at the source to minimize the potential of water damage.