Sleep is an excellent field but is rapidly changing. It is becoming more expensive. Medicare recently re-defined who qualifies for PAP therapy, which has caused much wailing and gnashing of teeth among providers. Many states are requiring licensing for techs, who are your lifeblood. Medicare requires independent labs only employ registered techs.
I'm an RPSGT (Registered Polysomnography Technologist) at a sleep center. We are one of the larger labs around at 11 beds. We never have an empty bed. Most labs are 4-6 beds and employ 2-3 techs (max 3 pts per night if AASM-accredited; this JUST changed this month, used to be 2 pt per night).
As a sleep doc, you can open a sleep center (includes narolepsy, parasomnia testing) that usually includes a clinical side for daytime visits. You can also open just a sleep lab, which only diagnoses and treats sleep breathing disorders. You can also be an off-site scorer, and charge $100-200 per study you score.
If you are in a well-insured area and develop a great base of referring docs (mostly PCPs, but also neurologists, ENTs, etc), you can make a ton of money. Your speed in scheduling new patients and getting them through the experience in a positive manner really affects your referral base.
To answer the other question, yes, you can get to sleep through MANY residencies -- IM, FM, psych, neuro, ENT, pulm and more. I'm partial to neurologists -- there's more to sleep medicine than apnea, which a lot of ENTs and pulm docs seem to forget.
