Question on filling a VP vacancy pre-1967

In the event of a vice-presidential vacancy (in this situation due to the death of the current VP) before the adoption of the 25th Amendment,

Would it have been possible for the sitting president to select a possible VP and issue an executive order placing him into that position? Would there be anything to prohibit him from doing so?
 
No, but by statute an office like "Deputy President" could be created and placed next in the line of succession. The Deputy President however would not have the vice-president's constitutional power to preside over the Senate.

"The Rockefeller and McCarthy proposals are constitutionally sound. This is because Congress has the power to create an office of First Secretary or Deputy President under the Necessary and Proper Clause of the Constitution, and the power to invest the occupant with a place in the line of succession under the succession provision. But Congress could not, by statute, give such an office the power to preside over the Senate (this is the exclusive duty of the Vice-President or, in his absence, the
President pro tempore). And the method of filling the office is limited: appointment by the President, by and with the advice and consent of the Senate, as in the case of any other executive appointment." https://groups.google.com/d/msg/soc.history.what-if/XHNn7NSAtLs/qkHhfmr2P5EJ
 
If I may be allowed a lapse back before 1900, this could have had interesting consequences in 1841.

If the office of Deputy President (or "Acting Vice President" or whatever) exists in 1841, presumably Tyler will wish to appoint one. Could this force a Court ruling on whether the office of Vice-President is actually vacant, or whether Tyler is still VP and merely acting as President, as some people argued at the time?
 
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