I've used the PI's built in serial port without any problems. The first step is to stop the Pi's OS from using it, so that you can use it for your own purposes.
Second step is (as Gordon said) to insert an RS232 level-shifter circuit in between the PI's 3.3V logic-level RX and TX data pins and the TNC.
Both steps are described here:-
http://raspberrypihobbyist.blogspot.co. ... -port.html
HOWEVER, the circuit in that article (using a MAX232 running from 5V) is bad practice for the Pi, as it means that the logic-level data output from the MAX232 will output 5V into the Pi's RX input pin. No external device should ever feed more than 3.3V into any of the Pi's GPIO pins.
There are some very small, neat RS232 level shifters available on Ebay ready-made for typically about 3-4 British Pounds, possibly a little more in US Dollars. The ones I bought recently are so small they fit easily inside a DB9 plug/socket shell.
Avoid those which use the MAX232 chip as it can only run reliably on 5V, choose one which uses the 3V-compatible MAX3232 chip - and run it from the 3.3V supply output pin on the Pi's GIO port, not from the 5V supply.
If you'd rather build your own, build the circuit shown on the page in the link above, but use a MAX3232 chip instead of a MAX232, and power the circuit from 3.3V, not from 5V as shown.
Although USB - RS232 cables may work just fine (like you, I've read that people have had a few problems with them) USB ports and USB bandwidth are a precious commodity on the Pi, so I would tend to go with the onboard serial interface as that consumes neither and leaves them free for other purposes.