Last year I went as Chaplain to a school trip to Rome and the (rather anti-Christian) guide we had at the Coliseum repeatedly stated that no Christians were killed in the Coliseum.
Thinking of the devotion shown by St Therese of Lisieux, this didn’t seem very likely to me.
Also, there is a book on the subject:
Also, Pope St Gregory the Great gave sand from the Coliseum as a relic…
Were some of the early Roman Martyrs killed in the Coliseum?