APA bows are fully tunable without a press or any special tools. They're designed such that the cams can be partially rotated and pinned in place to take tension off the string or cables while you make adjustments.
I don't know of any other bows that can be fully tuned without a press. You can adjust cam lean without a press on some of the newer Bowtech and Elite models, but you still need a press to adjust cam timing.
ETA: Some of the newer Bowtechs do also have press-less cam timing adjustment ("TimeLock" feature) in addition to press-less cam lean adjustment ("DeadLock"). A press would still be needed to adjust cable twists, change string/cables, and install a peep sight on these models. If you're serious about wanting to do your own tuning, get a press...don't limit yourself to the very few bow options that can be tuned without one.