Sometimes, it can feel almost impossible to both get the collectible card and get a golden crown time in the same run. The trick is this: You don't need to do both in the same attempt.
The collectable cards will always show your best crown score. This means that you can take your time and grab the card, scoring you a bronze crown in one go. But now you have the card registered in the card album. If you play the level again and achieve a golden time, the card will simply update to reflect this - and you don't need to collect it again.