I have to make a rocket for school and we get extra credit if we don’t use tape.
It’s hard to say what will work best given the limited amount of information in your question, but assuming you’re using light weight plastic in the construction, here are some suggestions. You’ll need to experiment and see which works for you.
Alternative air-tight adhesives to consider:
Candle wax. Light a candle and drip wax on rocket where you wish to seal it. Hot wax also functions as an adhesive.
Surf wax. Rub this and build up a coating where you want have an airtight seal. It’s tacky, too, but you’ll need to experiment to see if it’s sticky enough.
Silicone caulking. Strong, flexible seal but you’ll probably need a clamp to hold your rocket together while this dries to make sure it adheres correctly.
Sugru. A silicone clay that you mold into shape and let dry. Be sure to press it smooth to ensure an airtight seal. Probably your best bet. I’d try this one first. You can get this at Target or on Amazon.
Sounds like a fun project! Good luck!