A ‘eulogy,’ despite its association with melancholy settings, is meant to offer praise. A eulogy should celebrate the achievements and character of the person who has died.
An ‘elegy’ is referring to something that expresses sorrow in a reflective way. It can be presented in any work that considers a subject with a sense or reflection or melancholy.
So if you are struggling to write something then your eulogy can contain an elegy.
How to introduce a poem in a eulogy?
Good lead ins to reading a poem by another author can include short statements like “This poem by ____ always reminds me of ____ because they both so loved life,” or “In honour of ____ I would like to share one of their favourite psalms/songs/poems/etc.”
‘Elegy’ vs. ‘Eulogy’
How to speak about what is lost
https://www.merriam-webster.com/words-at-play/elegy-vs-eulogy-difference-usage