Ha! I just replied to another thread (maybe yours? ) about anyone familiar with parrots will think pigeons are *easy*! Perhaps I spoke too soon?
Pigeons lack any facility to cause you harm, except via allergy / lung irritation via their feather dust, of which there is a lot!
A single pigeon will require significant interaction from you, a pigeon friend or two might be nice. However compared to the demands for company that a parrot can make, entertaining a pigeon is probably light work.
The pigeon needs a mix of seeds and legumes. The one that
@CCsGarden recommended looks fine to me, and in pretty certain that she's had a long history of success with it.
I've also fed mine several different chicken feeds, mostly on the recommendation of the gentleman who sold me the birds. But do check the label to see that it includes some Methionine and Lysine if you go that route. Pigeons will consume in the range of about 1 to 2 ounces of quality feed per day, so that 6 lbs bag that CCsGarden linked is a month and more for a single bird.
Pigeons are quite forgiving, both with respect to their care and behaviorally. Spend time with the bird, and likely what you've known with regards to your parrot will apply here as well. The exception being that if a parrot becomes frightened, it can inflict a nasty bite. If a pigeon becomes frightened, flight is is only choice. Keep that in mind, this bird feels that distance is its only protection. If you get up close and personal and it suddenly decides it has made a mistake, it can't warn you off with its beak. A pigeon bite carries less threat than a Bantam chicken bite. That means getting over that initial hurdle of close proximity requires a greater level of trust than with the parrot.
Folks raising pigeons in purpose made lofts can "cheat" a little. Limit the height to 6 or 7 feet, whatever precludes the birds from flying over you easily. Limit the width to about 4 or 5 feet, so there is no easy way around you. The loft can be as long as you like. Now the bird is forced into close proximity, and you can tend to them and be in the cage, and that initial hurdle is quickly over come.
In the home you might approach this, as has been mentioned, by using a large dog crate. Do this for part of the day, or 100% of the time for a week or two. Then allow whatever your normal fee range is (room, aviary, whole house, whatever). None of which is likely necessary, you can just take time, patience and persistence and achieve the same or better effect.
All the best of luck!