Technically a "morning room" is just a sitting room. You can put anything you want in it, to be very liberal, seeing as it is your home. However, anything that makes it an inviting place to sit would be a direction I would suggest.
What style is your home? You can make it very chic or relaxed or formal, and from there more specific design ideas can be given.
You can also find a ton of ideas here - https://www.houzz.com/photos/morning-room-phbr0lbl-bl~l_38655

My morning room was used as casual dining. Small table for 4 someplace to throw down coffee and do homework. I kept the dining room table more formal.

I'd never heard of a morning room until another Houzzer asked advice on the layout of theirs and realized I had one too! I have a casual dining table in mine and will have a reading corner with a comfy chair. Some of my neighbors with the same layout use theirs as the TV area and keep their living room formal.

In Downtown Abbey times (and before) a morning room was a small drawing room to receive visitors before lunch (a drawing room was after lunch). Ideally the morning room was placed on the East where the sun shone in the morning and the drawing room to the other side. Ladies could read, sew etc using the available lighttechnically what you have placed is correct for both purposes but Edwardian times didn't have open plan!! Maybe you can zone your home using spacers and room dividers?

Really, it’s up to you. Ask yourself how the space will best fit your needs. Do you have casual family gatherings? Then consider a trestle table with comfy seating. Does your family like to gather together around the TV? The set the room up as an entertainment space. Do you do crafting? Make it a craft room. Do you like to read? Make it into a reading room. The goal would be to have a space that fits your needs.

I think a nice relaxing space to have your morning coffee and read the paper or sit and read a book in the afternoon.