I would find a place on the transom or a compartment wall as the two you mentioned do not do well with heat and or electricity!  Mine is on a support structure with little to no movement.

How about on the underside of the compartment lid? ???

Probably because of the heat rising around the unit.  Electronic type chargers, which don't generate as much heat a conventional charger style, can be mounted in any position.  
Examples of these types are Guest, Stealth, and Motorguide

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Of course it's electric.   I said electronic vs. the type that use coils and transformers internally.  These types of on-board chargers are often refferred to as "Traditional" chargers.  They will work fine, however they are heavier, generate more heat, and usually don't have the number of charging stages that an electronic type has.  This factor can often affect the total charge a battery actually gets that reads fully charged.  It also can affect the lifespan of a battery.
There is a good article in Bass & Walleye Boats magazine this month about the different brands of chargers on the market.  They tested 7 different ones and the results are surprising, to say the least.

  I mounted my CSI unit (waterproof, and recommended) on the cover over the bilge. I would avoid putting any fasteners into the transom...if they leak, and if you have a wood core transom, it's trouble. I don't know what kind of boat you have, or what charger you bought.  If one corner cannot be bolted down, maybe a spacer and longer fastener would help, or a bracket of some sort. More info would help.