Are there any truly effective self-paced piano teaching programs available for beginners?

I have always wanted to learn how to play piano, but have very limited time and an erratic schedule. How can I go about learning at my own pace and in the privacy of my own home?

Try the faber Piano Adventures series for Adults. You can ask for it at your local sheet music store, or find it on http://www.fjhmusic.com/piano/apa.htm

I would suggest you to look for a teacher who might let you come to a lesson once per month. Not many teachers would allow, this but some may. And it is crucial you have some instruction from a professional. You may not realize some bad habits you may develop (incorrect hand structure, posture issues, rhythm issues) and you’ll need someone there to correct those before they become permanant problems.
You may like to search for a teacher on one of these sites:
http://www.musicstaff.com
http://www.pianoteachers.com
http://www.mtna.org

Good luck to you, and enjoy the piano!