Scalar positronium decay Feynman diagram Charged scalar particles appear in some Beyond the Standard Model theories and are regularly searched for at high energy colliders.
For positronium there is a simple Feynman diagram as shown below

Would the same diagram work for a scalar charged particle-antiparticle bound state? Unfortunately, if we try to apply this diagram to such a state we have a problem with the spin conservation being violated. What is the Feynman diagram for scalar charged particle-antiparticle bound state annihilation?
 A: There (only) 2 possibilities for the spin state of a positronium, that is the singlet state S=0 where the spin of electron and positron are anti-parallel which is called para-positronium
and the $S=1$ state where the spin of electron and positron are parallel which is called ortho-positronium.
Each case of both cases has to be treated differently.
The para-positronium decays in 2 photons as shown in the Feynman-diagram of the post, while the  ortho-positronium decays in an odd number of photons, preferentially in 3, but 5, ... is a priori also possible but very unprobable.
So if you consider a $S=1$ positronium (ortho-positronium), then you have to compute a Feynman diagram with 3 out-going photons. The third photon is emitted from the virtual exchange particle between the 2 vertices of the Feynman diagram already shown in the post.
If you want to consider a positronium in scalar electrodynamics, there is chapter 61 on this in the book of Srednicki
http://web.physics.ucsb.edu/~mark/ms-qft-DRAFT.pdf
Figure 61.2 shows the Feynman diagram and at the bottom of p. 366 the calculation is shown. If the ingoing particles are scalar, the computation is very similar to the decay of the Parapositronium, the singlet state.
But the in-going particles of the "positronium" are no longer electron respectively positrons.
To recap the Feynman diagram is the same as the one shown in the post, only the in-going particles change to scalar. These particles could be for instance supersymmetric particles. But such particles would hardly build up a bound state at least for a very short time, therefore one would not call it a "positronium".
When it is all about the spin state of virtual particle note that spin is not conserved. The virtual particle in order to fulfill angular momentum conversation can adapt some orbital angular momentum in order to fulfill angular momentum conversation. Anyway, it is a virtual particle, whose physical quantities are not measurable. What counts at the end is that angular momentum is conserved between the in-going and the out-going particles. This can be easily achieved for in-going scalar particles as described above.
