Kliff; first of all, good luck and congrats for going down this route; you'll probably learn a lot, have some fun, and even make your wife happy in the process. (Sounds like a win win win situation to me!)
In most cases with voice and piano alone, you're better off doing everything together, live in the church/hall. Overdubbing is a lot of extra work, and perhaps not worth your time for what your doing. (Seriously: Will there be a click track? Solid, countable intros? Who leads, the singer or the accompanist? Are they professionals? Many non-pros can't handle overdubs in a free-form situation like solo piano and vocals-after-the-fact. It could be VERY tricky if your wife hasn't done this sort of thing before. )
Any good accompanist will want to work with the singer LIVE, so they can breath & move together musically. The cues are sometimes visual, sometimes undetectable, but they ARE there live, and they'll get lost when trying to overdub. (Again, it MIGHT work, it might not.)
If you really do only have two mics, then put one on the piano, one on the singer. (Don't know your mic choices, so I can't really say which goes where...) Hopefully it's a fairly large room so one wont be blowing out the other, sonically. Let them practice while you set up, and get comfortable with their blend together, IN the room. Have them position themselves recital-style, with the singer slightly out in front of the piano, with the crook behind her.
Mic to taste inside the piano - with only one mic, you're going to have to split the difference in terms of best placement and get the best sound overall. If it's a cardioid, it will pick up the piano and reject the singer (who's back is to the mic anyway) behind it.
I'd recommend opening the lid either full or 1/4 stick, even though there's a chance of bleed into the vocal mic. A good accompanist can work with this, and you can even try moving them a little farther apart. (Remember, you WILL get bleed, that's all part of the equation.) You may have to move the singer a bit farther away from the piano to get a clean (but NOT isolated) sound, and I'm betting they will want to be in visual contact with each other, however you position them.
You may need a windscreen for the vocal mic (esp if it's a true condenser mic of either size - LD or SD) and where it goes will have to be according to taste. For traditional classical and jazz singers, I like 3-6 feet away, sometimes a little above the mouth/jawline (mostly to prevent pops and blasts, otherwise I'll use a popper stopper. Again, this is going to be according to taste. If your singer is using a music stand, there's another space issue there. (Watch out for harsh reflections off a metal music stand, as well.)
Later, in mixdown/software mode, you'll probably find the mics/channels are a bit dry this way, so add reverb to taste, esp since this will have been a fairly close-mic'd situation on location. I'm guessing you'll want to create a sense of space around the performers, recreating the sonic environment - a "Live" sound, as opposed to a dead studio.
If your budget ever expands, you can always put up some ambient mics (spaced omni pair, etc.) and see if capturing the room sound around the musicians helps you any. (On a separate track, of course) Studio Projects (SP microphones) Makes some great stuff, the C4's are sold in pairs, with two capsules each; one cardioid and one omni, all for about $350 nowadays. (New pricing coming out, I think?) These are a GREAT pair of starter mics for you as you learn and grow.
Good luck, let us know how it goes.
