C is prolly the lowest practical threshold for standard acoustics with typical strings. Yet if you play that low frequently you might try heavier sets of strings to give em more tension. Floppy strings won't give you as much consistent note frequency, being much more sensitive to fret pressure and picking attack, which may be contributing to your tuner problems. If I'm using a tuner when I tune to open C, I'll just use it for one string (allowing time for stretch), and use that string as the reference for the others. Also, depending on the tuning you're going to, you probably already have reference strings in standard tuning that are "friendly" notes with that key. Like for C, the open G string should be harmonious...if not, the waves of dissonance will be apparent.

And oh yes, tuners can be more versatile for those ranges, but they can get expensive. Maybe just get a tuning fork or 2 for those reference strings mentioned. They're cheap, reliable, don't break, and don't use batteries.