It can't be $\Delta^-$ since that is another particle also made up of quarks (not antiquarks). I can think of four possibilities:
- $\overline\Delta^+$
- $\overline{\Delta^+}$
- $\overline\Delta^-$
- $\overline{\Delta^-}$
I am sure someone has asked a similar question, but I failed at searching for it.
Answer
The $\Delta$ is a quartet of particles with isospin 3/2: $$ \Delta^-, \Delta^0, \Delta^+, \Delta^{++} $$ I would expect the anti-$\Delta$ to be written $\bar\Delta$, with the four isospin projections $$ \bar\Delta^{--}, \bar\Delta^-, \bar\Delta^0, \bar\Delta^+ $$ In this case the antiparticle of the $\Delta^+$ would be the $\bar\Delta^-$.
If you'd like a canonical reference, look for a paper about pion production with antiproton beams. Note that there's a whole spectrum of $\Delta$ resonances, not just the lightest one at 1232 MeV.
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