There are a few ways to fix this with the best being a new unit but out side of that as you stated you wish to avoid that right now I will list a few tricks I have used in just cases like this 1) Try tighting the fittings a little bit but be careful as they are in plastic! 2) wrap in Teflon tape at lest 3 to 4 wraps but no more then 6 as it may not fit back in with that many . Normally 3 to 4 will do it.
3 pull the lines( there your auto tranny cooling lines by the way) and use a tight fitting rubber washer on the out side next to the hole then wrap the threads with Teflon tape 3 to 4 times and tighten it up. If none of this works buy a new radiator as using stop leak is never a good deal if it can be avoided at all as not only will it stop the leak (maybe) but because of how it works it can also plug or come close to it the small tubes in the radiator and or heater core besides coat the cooling passages in the motor lowering there efficiency. Now if you do replace the radiator do your self a big favor and do these things also 1) Flush the motor and heater core before you install the new radiator do this by removing the thermostat and then run a hose into the return radiator line from the motor tell you get clear water.
2) Replace thermostat with a new one 3) Replace all radiator hoses and heater hoses including any small by-pass hoses. 4) Replace the radiator cap with a new one that also is with in the OEM pressure rating. Doing the above will stop any contamination from getting into the new radiator right off the bat.
It will also stop you from blowing older hoses that may be weak from the possible higher pressure of the new radiator being it will not longer be leaking and can now build full pressure some thing it most likely has not done for some time. (Learned this one the hard way on the side of the road late at night as one hose after another blew!).
Go to an auto parts store such as O'Reiley's and purchase the O-Rings for the fittings...they are cheap....the old ones have dried up due to heat and age.....cheap fix... I replaced mine when I installed a new radiator....