In Diplomacy, is it possible for an army to be convoyed by two countries if both write the appropriate orders?
It is possible for an army to be convoyed my multiple countries (although you should write the orders differently than you did in your example).
First, the relevant rules:

Convoying an Army Across Several Water Provinces
If Fleets occupy adjacent water provinces, an Army can be convoyed
through all these water provinces on one turn, landing in a coastal
province adjacent to the final Fleet in the chain.
In Diagram 20, the English Army from London goes to Tunis on a
single move with help from the French player.


Italy would need to write the orders:

A Ven to Tun
F Ion convoys A Ven to Tun

And Austria would write the order:

F Adr convoys A Ven to Tun

From the rules:

Writing Convoy Orders
Just as “S” indicates support, the letter “C” is used to indicate convoy.
Following is an example of a convoy order:
A Ank–Sev; F Bla C A Ank–Sev

The reason for this is that you can potentially issue multiple convoy orders:

An Army convoyed using alternate convoy orders reaches its
destination as long as at least one convoy route remains open.
Orders can be written to permit more than one route for convoying
an Army from its origin to its destination. The Army isn’t prevented
from moving unless all routes in the order are disrupted.