Will Kohl be the rock of W. German stability?

How stable will West Germany be for how long under new conservative Chancellor Helmut Kohl?

The question is puzzling both foreign diplomats and domestic commentators less than a week after Mr. Kohl replaced Social Democrat Helmut Schmidt, the first chancellor to be removed from office by Parliament in the federal republic's 33-year history. And many feel the disputed move to switch governments without giving the voters a say may have hastened a process of instability that could change the country's political landscape.

Mr. Kohl's first promise after taking power was to pursue middle-of-the-road consensus policies. And he made clear his top priorities were domestic - to get a sagging economy moving again and prevent a further rise in unemployment. Although he is, in his early 50s, the youngest West German chancellor, there was something unashamedly old-fashioned and nostalgic about his appeal for a revival of the ''reconstruction spirit'' which helped to rebuild West Germany after the devastation of World War II.

His center-right administration of Christian Democrats and Liberals, whose desertion of Mr. Schmidt provoked the switch, plans to enact an austere 1983 budget. This calls for welfare cuts, higher taxes, and extra incentives for business before seeking a mandate from voters at an early general election next March. Mr. Kohl's economic advisers hope that a short-term investment boom will have generated a new national mood by election day and ensure that the chancellor sweeps back into office.

But there are many ''ifs'' in that calculation, and some of them already seem to be working against the new center-right alliance.

The change of government in Bonn has not brought the national sense of relief that its authors had expected. According to opinion polls, most West Germans feel there was something dishonest about overthrowing Mr. Schmidt without an election, and few expect the new administration to make a better job of solving the country's problems. By setting the new election date in advance - a condition for the Bavarian Christian Social Union voting for Mr. Kohl - the center-right leaders have reluctantly unleashed a five-month election campaign on West Germans, in which every parliamentary debate, every local election, and every television interview is viewed as a test of what will happen on March 6.

The Social Democrats have emerged from the Bonn government crisis far more united and more popular than they have been for the last two years. If they can persuade Mr. Schmidt to run again for chancellor next March, they may be able to postpone their internal debates over economic and nuclear strategy until after March 6.

The Free Democrats, who began the year reasonably united in coalition with Mr. Schmidt, have been seriously torn by party leader Hans-Dietrich Genscher's tactical maneuvering toward the right and look unlikely to recover in time to avoid being completely defeated in March and losing all their seats in Parliament. Their place as West Germany's third political force is already being taken in the provinces.

The back-room wheeler-dealing that led to Mr. Schmidt's removal undoubtedly boosted the environmentalist Greens' arguments that the ''established'' parties were corrupt and unprincipled. And the Greens and peace campaigners will feel less compunction about opposing a conservative administration than they may have done in fighting the Social Democrats.

Mr. Kohl's staunch pro-Americanism may make an easier target for protesters against NATO plans to deploy new US nuclear missiles here next year than Mr. Schmidt's more critical attitude to the Reagan administration.

The Social Democrats have already served notice that the plan to site cruise and Pershing II missiles here unless Moscow gives up its medium-range missiles first will be an election issue in March. As long as Mr. Schmidt is still there, the majority of the party will ungrudgingly go along with the disputed strategy. But once he retires, the mood in the Social Democratic Party could swing fast toward at least a delay in the deployment.

The other major uncertainty that shrouds the start of the Kohl era is how the trade unions will react to his government's austerity plans and calls for stringent voluntary pay restraint. Under the Social Democrats, the unions were already girding to take to the streets over milder cuts in social security benefits. While the country's 17 labor unions are not overtly political, they are unlikely to grant the new administration a ''special honeymoon.''

So the West Germany that votes next March is likely to be a country with a changing party landscape, growing social unrest, and a mounting antimissile campaign outside the conventional party structure.

The challenge for Mr. Kohl is enormous and many commentators, long skeptical of his leadership talents, doubt if his blend of homely provincialism and moral self-righteousness can give the country the ''new beginning'' that he has promised.

But Mr. Kohl has surprised his critics before. He has demonstrated a rare talent for political survival and could yet confound those in his own party and in the media who see him as a weak king surrounded by unruly barons.

Much will depend on whether the new chancellor can steer the centrist course he has promised by playing the Liberals off against the unruly Christian Social Union of right-wing Bavarian state premier Franz Josef Strauss.

Mr. Strauss, who makes no secret of his ambition to run Mr. Kohl's government for him as vice-chancellor and foreign minister, is hoping that the Liberals will be wiped out in the election next March.

If that happened, the new chancellor would become the prisoner of his own barons and West Germany would be a much less stable place.