Germany was already bound by the so called "Paris Agreements" never to produce atomic, biological or chemical weapons (Protocol No. III (and Annexes) on the Control of Armaments, October 23, 19
http://avalon.law.yale.edu/20th_century/we005.asp#154).
Since 1961 § 17 of the German War Weapons Control Act explicitly forbids the development, production, import, export, transport and possession of nuclear weapons in any form or kind. § 16 excepts only those nuclear weapons which fall under the NATO. § 18 includes the same ban on biological and chemical weapons. Keep in mind that this act was decided upon by an absolute majority of the CDU/CSU which supported nuclear armament and during a period of growing tension with the USSR.
Therefore you will need a PoD long before 1961 to get there. Since remilitarisation started only in 1954 and the PoD should not be before 1947 there is only a small window to accomplish a complete reversal of the mainstream thinking to support such an act. One hast to consider that remilitarisation in itself was already a hot issue and faced hard resistance. Germany learned its lesson one might say and I am glad it did.
At last one has to consider that the German Bundeswehr was nuclear armed via the "nuclear sharing" since 1958. There was no need for the Allies to allow Germany to produce its own weapons.
I consider this possibility highly unlikely. Perhaps if the Western Allies would need German help for their own production (for example financing the French project as already suggested) and with Strauß as secretary of defense there might be a small opportunity. At least this will cost the CDU/CSU its absolute majority in the elections of 1957, although it may still stay in power perhaps in a coalition with the DP. How the Western allies come to need German money or other help so badly to allow them an atomic weapons production of their own with a PoD as late as 1947 I cannot conceive.
Kind regards,
G.