I agree with Kyril on this 100%. When I play a manpower-starved country I focus on higher cost but lower manpower forces wherever possible. Tac bombers are great force multipliers, as are arty or engi brigade attachments (when playing CORE). I build tanks instead of mechs or motorized, and if playing a coastal country where most of the provs I will be after are also coastal I might even build a few battleships. Although all of these forces are more expensive in IC and time to build, they require very little manpower.
To expand on the brigade thing, this is a strictly CORE adjustment. In vanilla attaching brigades costs extra manpower, but in CORE they do not. So when playing a low manpower country, I never build an infantry division without either an arty or engi brigade attached. Mostly I use engi brigades since they get a speed bonus, river crossing bonus and a defensive bonus. But I often build a few arty attachments to form the "fist" of my offensive force, sacrificing speed for firepower. I don't do this, however, unless I can also afford to research the arty tree or I am a member of the Allies. When I am allied with the Allies, I only research the theoreticals and a few of the enabling techs and let my allies give me the specific applied arty techs. When a member of the Axis or Comintern, you don't have enough countries allied with you to be able to count on getting any tech gifts.