If you're not trying to get something extraordinarily challenging like underground-access tickets, I think you've got a good chance of being able to snag your own tickets from the official website. However, you must be willing to set an alarm and get up in the middle of the night to get to your computer a few minutes before tickets begin to show up for the day you're interested in and remain there as other blocks of tickets become available until you're able to buy what you need. Others have reported success doing that on this forum. You may find a few such reports by scrolling back through this forum or using the Search function. You don't need to look back before January of this year, because sales procedures changed then. It would also be smart to do a practice run or two before your D-Day. I don't recall whether there have been reports of credit-card acceptance issues on the Colosseum website, but we hear about that issue for some sightseeing tickets. I'd have every credit card and every debit card I owned in front of me before trying to buy hard-to-get tickets like this.
If by chance PayPal is an option, that is almost guaranteed to work; PayPal will allow you to charge to the same credit card the ticket-sales website refuses to take. Be sure to indicate you want to pay in euros; PayPal would really like to charge you in dollars so it can make a nice profit by using an exchange rate that's bad for you.
If you are unlucky and end up empty-handed, there remains the possibility of going to the walk-up ticket booth over near the Colosseum. I believe all members of your party have to be there, and you may not get tickets for immediate entry, but it is possible you will be successful there. I assume it's best to go there early (I don't know when they start selling tickets).
I know the only way to get access to the underground area is on a tour. The same may be true of the upper level. So you need to stick with your guide to see those areas if you buy a tour that includes one of them. For the generally-open area of the Colosseum, I don't see any reason why you couldn't just wander off as soon as you're certain you've passed the last ticket check-point. Folks fairly often comment--not specifically about the Colosseum--that they were unable to get plain-vanilla tickets to a high-demand sight and English-language tours were sold out, so they bought tickets for Italian tours and just ditched the tour as soon as they could.
