Look for prepaid credit cards at local drug stores or similar places. They are everywhere over here. Basically you pay a certain amount in cash at the store and they give you a card loaded with that amount.
When it is depleted you can go back and have it reloaded or just get a new one. Sometimes they are already set for predetermined amounts. Like 25, 50, or 100 of whatever your currency is.
If all else fails then you will have to pucker up to Mom and/or Dad to let you use theirs.
Sometimes Grandma may be a good option also.