IPA: /dɪˈzaɪərəsli/
KK: /dɪˈzaɪərəsli/
In a way that shows a strong wish or longing for something.
She looked at the beautiful dress desirously, wishing it were hers.
Desirously → It is formed from "desire" (from Old French *desir*, meaning longing or wish) and the suffix "-ously" (meaning in a manner characterized by). The word "desirously" means in a manner characterized by longing or wishfulness.
Think of someone acting in a way that shows their 'longing' ('desire') — the '-ously' indicates how they are expressing that longing.