a couple of notes and suggestions:
1) just because you get the note that you've been outbid doesn't mean you have no chance at the coach on the current offer. The guy who has the #1 offer may have #1 offer on 3 coaches. He can only sign one, then his offer to the other two get pulled and you now have #1 offer. And if that guy was signing this cycle, you may be able to sign him without ever having the #1 offer. I wouldn't rely on this happening, but it is a reason for leaving an offer outstanding if you don't have #1 offer
2) for MLB coaches, after the re-sign period, see how many teams need a given coach. Then count down that many names in the list of coaches. That sets the bar for the "worst" coach you could end up with if you waited until the end. Use the gap between that guy and the top guys to decide whether you want to chase the top guys or value shop for the scraps (I almost always value shop)
3) related to point 2, do that same anlysis before you re-hire last year's coach. Sure it is a sure thing and an easy thing to re-sign that 84 HC for $2.5M, but if there are 35 MLB HCs rated above 81, you can get a guy in the low 80s for a fraction of the price
4) minor league coaches are a bit more of a pain, but they matter less and most people don't care so much, so just make an early offer to a mid-level guy for slightly over his asking price, and nobody else will bother to try to out-bid you, they will just look for other low-hanging fruit
5) another thing not to count on, but it happens, is that if all coaching spots for a given level get filled early (i.e. before the last cycle), the remaining guys drop their demands a level. So it is possible to get a "MLB" coach for you AAA team. I say not to count on it beacuase there is usually at least one owner in each world who is waiting until the end to value shop a MLB coach, or own absentee owner who isn't making offers to coaches. But it can happen.