We are at a big church (not a mega church though)---
Some of the things I have seen them do that may or may not convey to an off site fundraiser:
Candy bouquets--sold for $6 at our Church musical for Valentine's day--it was skinny dowel rods wrapped in a cellophane wrapper like a bouquet with candy being the "flowers"--you might be able to do this at a
Walmart type place Mother's day weekend. ANYTHING you do at walmart, please make sure the kids are actually selling something and not simply begging.
I distributed Mardi Gras beads in red/silver/blue over 4th of July weekend as a fundraiser for the LLS/Team in Training....always think out of the box and if you can theme it, it works a little better.
Cookie dough sales are coming up...for our youth group. No idea who they are doing this through.
Some type of Parents night out---hosted at the church and the teens watch the kids from like 6-10 while parents get a date night.
At another church, I saw that they were offering "rent a teen" to do odds and ends work at people's homes--to include washing their car, mowing the lawn, housework or whatever. It was set up for a 2 hour period. Not to be confused with "renting a slave"--you would want to be clear about the service being offered and the way they did it was the person doing the renting would disclose what was needed.
Additional things--that work if you can get items donated....
bake sale (homemade, not store bought

)
"dinners"
"breakfasts"--like a pancake breakfast after services.
Around here, they have to have a "to code" kitchen to legally do these things. We kind of got away with it iin the past--but when we got the new building and updated commercial kitchen, these events always have to be o nthe up and up. So if that is the case at your church, just be aware of that.
Some more creative ideas....
Flamingo flocking--people pay you to flock people's homes with those tacky lawn ornaments and then you can offer a removal service (but include something that also indicates that the donation is voluntary). Works well by referral only...and disclosing who had their yard infested.
Be creative, have fun--and for life experience, begging is not the answer. Much more effective if the teens are working for it.