The best way to get people to do a job is to pay them enough that they choose to. If people are not choosing to join the army that means they are not getting paid enough. The government has the power to coerce people into doing things and the preferred way of doing this in this case is taxation. Make everyone contribute to the war effort and let the market choose who pays in cash and who pays in risk of bodily harm but is compensated financially.

In fact, the neither the central government nor coercion are (in principle) required. A sane country could rely on the country purely for it's role as a contract enforcer and solve such cooperation problems through normal market forces and assurance contracts. "Military Kickstarter" as it were. This of course generalises to an outright weirdtopia.