Many kids in my generation and more so in my parents and grandparents' generations grew up with real work to do. When my kids were little I was one of those people who was afraid of making my kids work "too hard." I didn't want to use them for "slave labor." I didn't want to make them do the things I didn't want to do so I didn't have to do them. Whatever...
At this point in my life I think that if you fall into that kind of thinking you miss the fact that God made us with plans for work*. Doing a good job has it's own intrinsic rewards. Being able to do something you love and get good at it, have others notice and ultimately have others ask you to do the job because you are so good at it is rewarding in itself with or without monetary compensation.
On the one hand you're trying to build a good work ethic in kids that will grow and carry them through adulthood (including doing a job just because it has to get done.) On the other had you're giving kids the privilege of work that can be just as meaningful for children at any age as it is for adults. Work grows self-confidence and self-worth. A child feels needed. They have an important job to do. They have a way to contribute to the good of their family unit.
Children can earn privilege. They can work to earn the privilege of more and more responsibility by remembering a chore, doing a good job, doing an extra good job. They earn trust.
If you have a group of kids working together you very quickly figure out who delegates, who manages, who manages shrewdly, lol! As kids grow, maybe they earn the privilege of doing the jobs they love most, and doing the things they're best at by doing the jobs they hate with a good attitude.
So what can toddlers do? Break down the jobs you do as a grown up.
Washing plastic dishes.
Folding towels and wash cloths.
Putting plates by each chair.
Putting napkins on a table.
Handing out programs.
Putting a Bible on each chair.
When I was old enough I sat by my mom when she played the organ and turned the pages. Even before I could read music she would nod and I would turn the page.
Picking wild flowers or garden flowers and bringing them to someone who is sick.
Running water in a plastic vase.
Spreading peanut butter or jelly on a piece of bread, though you may not want toddlers working with food for other people except in small family-type groups.
Passing out cookies.
Passing out paper cups.
Picking up empty communion cups and then washing hands.
Washing hands and putting out communion cups.
Helping change the colors on an altar or helping set a communion table (standing on a chair)
Picking up old programs or papers and throwing them away.
Handing out pens or pencils
Holding a collection bag
Putting new candles in candle holders
Blowing out candles
Putting out music folders for musicians. Why not paste or draw a picture of the instrument on the front of the folder and let a toddler put it on the chair by the instrument. (Yes, you walk with them so they don't knock over the guitars. Maybe their reward is hitting the drum a couple of times when they finish. Why not?)
All of this - not alone but helping a grown up. Look at all the grownup jobs people do at home or at church. If you have a toddler, a pre-schooler, an elementary aged child, a pre-teen, or a teen by your side - what can they do to help?
Maybe they won't do it the way you do. If you're not hounding them all the time and you make sure you praise them for details well done, you can correct and adjust when you need to. Just don't discourage them. Be grateful.
Pair older people with younger people. What about pairing people who can't hear well with younger children - or children who like to talk loud. You'd have to train these young ear-pieces. (Not during worship but maybe for the before or after fellowshipping.) It can still be too loud but you get the idea. What do older people find hard that little people can do for them? Bending over? Picking things up off the floor?
As I say, you get the idea. Use your imagination!
* Interesting to read this passage in context, thinking about work. It seems a contradiction but apparently it isn't. And there's Romans 12:1. Again, go back and read the passage in context (the whole chapter) thinking, not just about spiritual gifts but about the physical work we do with our bodies - our spiritual service of worship. Then bring children into the picture and see what God will show you.