It's unlikely that groups.io will ever provide a "print table" feature - the formatting options are as numerous as the number of people using databases.
Two thoughts -
- You say you create a database of the year's events/items - Why not generate a PDF report (using Excel for example) of that year's info for members to download and print?
- "reproduce part of the ... database" - If what you want to copy/paste is on one page, try selecting the rows of interest, copy as plain text into Word, select the text, Insert Table, Convert text to table (separate text at Tabs). Should give you a table to use for the subset of the data needed.
Just some ideas that might make things easier until when/if groups.io provides some facility to do what you're looking for.