Colosseum underground

No. The colosseum underground tours are offered on every day of the week. You need to read Rick Steves Italy and/or other guidebooks, make a list of things you want to do on your trip, turn your list into a day-by-day itinerary, figure out which day you would like do your tour, check the website of the tour operators, pick an appealing tour, reserve your spot(s) and pay, and type your tour time and meeting place in your itinerary. Print your itinerary and all your tour confirmation pages, before your trip, put the printouts in a pencil case, and carry it with you in a smallish day backpack along with a bottle of water and anything else essential. My colosseum underground tour was with "The Roman Guy", in July 2017. The tour worked out fine.

Jen, just the heads up that underground tours are THE most difficult tickets to try and obtain in Rome, and especially during high season due to the ratio of people who want them and the limited amount available.

Yes, you can go through independent companies, like the The Roman Guy mentioned above, for these being aware that they'll cost more than booking through the Colosseum itself (https://ticketing.colosseo.it/en/) because they often include a guided tour of the Palatine and Forum as well; highly recommended. But there's no guarantee that the indy company can get hands on those scarce tickets either or for the time you'd booked. For instance, this text in the Roman Guy's website for their "Colosseum Underground Tour with Roman Forum and Palatine Hill" tour:
https://theromanguy.com/tours/italy/rome/colosseum-dungeons-tour-with-roman-forum-palantine-hill?itemlistname=the%20best%20colosseum%20tours%20in%20rome&itemlistid=22&index=2&_gl=1*qjfq50*_up*MQ..*_gs*MQ..*_ga*NzUwNjQ4ODY3LjE3NTI0NTE0NzA.*_ga_Y488PQCWM9*czE3NTI0NTE0NjkkbzEkZzEkdDE3NTI0NTE0ODIkajQ3JGwwJGgyMDY2OTEyMDE3&gclid=EAIaIQobChMI0OL3uIa7jgMVGDYIBR03Hx-DEAAYASAAEgL3W_D_BwE&gbraid=0AAAAADM-panpNkbUWcpYgONX7Uk_LexvA

Can my tour be canceled or moved to a different day?
Yes, it is possible. Colosseum Underground tours are very exclusive and are subject to changes, but we’re experts in this field and have staff dedicated to ensuring the best possible customer experience. If we are unable to acquire tickets on your behalf, we will let you know at least 14 days before your tour date, in which case we'll add you to a comparable tour or offer a full refund.

Is it possible The Tour Guy will change this tour time?
Yes, it is very likely to happen due to the exclusive nature of this tour. We recommend you keep your entire day open to accommodate your new tour time. Be sure to monitor your email as we will contact you at least 14 days before the tour with any new start time.