Yes, chromosomal or DNA level. Best Regards Václav

As pointed by dear Vaclav, You may design PCR primers specific for sexuality genes of plants if already known, or you may use degenerate primers designed based on the sequences of known sexuality genes in other plants preferentially of closer relationship to the plant of your study.

If You have still problem, check molecular DNA markers with the genomic DNA of both sexes and determine the differential bands able to separate the sexes from each other. The best molecular DNA markers (as a tool) and the resulted bands (as criteria) can be applied for further works with those of unknown sexuality. Also, You may be interested in the differential bands on the gels, then send them to be sequenced and blast the sequences in order to find out them. Anyway You may design new sex-specific primers based on the sequence of the resulted differential bands.

It is not always possible to evaluate the sex of dioecious plant looking at morphological or phenotypic characteristics of the plant species. In certain species, inflorescence length prior to its flowering gives an idea to know the sex of that individual plant, for example Excoecaria agallocha, Mangifera indica is the best example to evaluate the sex of the plant,- short-stature, robust look and crown-forming branching pattern indicate female plant while the opposite characters indicate male plant. Prior to flowering, one can assess the sex in this species

Some time back I have come across a thesis wherein while working on diversity of Coccinia grandis using ISSR markers, they came out with a particular ISSR primer which consistently helped them to recognise male and female plants. You may have to screen some ISSR primers which might work similar way for Papaya.