euro coins

You can make change while you are there. Buy thing in cash, you'll get some coins in your change.

Most of the pay toilets I encountered cost €.50 or €1, so you don't usually need smaller coins for that.

Buy an espresso and you’ll get the change.
Besides I rarely use pay toilets. I just use toilets at restaurants, coffee bars, etc. they are free for customers and usually clean.

And when you leave, hold onto those €0.50 coins -- we always like to carry "pee money."

At ATMs, chose an amount that will give you 20's, not 100% 50's. (240 vs 250). Break your 50 bills for larger purchases so you always have change and smaller bills. Smaller shops and restaurant may have difficulty (especially early in the day) giving change for a 50 note if the purchase is only 5 Euros. That being said always try to spend the copper coins; 5, 2, and 1 cents. Otherwise you will go home with a big handful. We find that many small shops, round the purchase to an even .05 so they don't have to collect the .01 and .02 coins.

Or, if you are ready for a break, stop in a cafe for a caffè, and use restroom for free. And McDonald's are always an option.

When asking where the restroom is, ask for "toilett" not restroom, and/or look for signs for WC. And good idea to have a tiny roll of toilet paper or Kleenex with you.. Many public restrooms have, but some don't.

We always carry a couple of dollars in coins with us (50 cent, 1 euro) just in case. Try to use the Toilet (WC ie water closet) before leaving a museum. We also carry half rolls of toilet paper( spent down rolls from home) with us in our day bag as well as individual packaged Wet Ones just in case. I also have some in my carry on or purse for the flight, Had more than one occasion on a transatlantic flight there was none left towards the end of the flight, especially if a full flight. I also carry a few paper toilet seat covers like the ones in the ladies room in Walmart, Home Depot etc. but you need to watch the septic systems in Europe as they are delicate. At the end of the trip if there is any change left we use it towards coffee or snacks at the airport when we leave. You might have under a dollar left when you leave- save it for the the next trip. There is so much to see- it will call your heart back. Have a great time !

Some places are 'by donation' so you have a little flexibility there. I rarely have paid for toilets, but do keep some change around.
My kids collected international coins so I always had some small denominations around for them. Now that they are grown, I still have the (heavy) collection and it has come in handy as I have been granted permission to raid it for coins for travel. So once you have a collection, you could bring a small amount home either for kids, or a possible return. It won't break the bank. I do tend to spend the smaller coins and the bulk of coins on the trip, however, as they cannot be converted once home.
More and more airports and planes are collecting coinage from travelers for charity purposes if you know you won't be returning.

You won't get coins from a bank (notes only) and definitely not from an ATM! But you will get them soon enough as change when you buy something with your notes.
Photos of coins here: https://moneterare.net/wp-content/uploads/2018/06/eurocollezione-1024x518.jpg

• 0.01, 0.02, 0.05 - brown, useless, you get them as change. Unless you count out an exact amount, difficult to get rid of. Some countries have abolished the 0.01 and 0.02 (but not Italy)
• 0.10, 0.20, 0.50 - gold coloured. Useful
• €1, €2 - Bi-metal. Very useful
• €5 - smallest banknote

The subdivision is officially called a "eurocent", but nobody calls them that, they have a different name in each language. In Italian they are centesimi.

After a day or two you'll likely find you've built up a big collection of coins from your change. Your issue won't be whether you have any for the lavvy but how to get rid of the more useless and bulky coins. By day 5 you'll be becoming more tip-happy and hoping for beggars at your cafe table so you can off-load some of them.

nope, no matter the coins in my pocket I never hope for beggers at my table

Easy solution. Get off your flight, go through immigration, stop at an ATM and get some cash (hope it is one that allows selection of smaller bills), stop at the airport coffee shop, buy a coffee, get coins back as change. Repeat the ATM and coffee shop part as often as needed.

You get coins the same way you do at home. I like to keep a minimum of a few 50 cent, 1€, and 2€, coins in my pocket for reasons already mentioned. More than that, and smaller coins get spent. But people who are unable or unwilling to count in euro, and just hand over paper currency and end up with fistfuls of small coins. I think that this is partly because US travelers are unfamiliar with the idea that there is no extra sales tax on purchases (its included in the price) so they are waiting to get a total amount that they dont understand. Just try and count up your purchases based on the sticker price, and you can get rid of excess coins.

Oh, if you're at a pay toilet where there is a dish for payment and a human attendant, you can make change out of the dish as long as the attendant can see what you're doing.

Thank you all for your replies and the visual aid is handy too!

On the way home, there's probably a charity donation container at the airport that will be happy for your small change