"I think many people have 'border line' paranormal powers." As such, trying to affect the outcome of events when someone else is involved pits my 'powers' against the other persons 'powers' and is harder to do. Of course they usually don't 'know' that they can have 'powers' to affect events.
You could find someone who is neutral as to the outcome.
On the other hand, you should be able to do it on your own. You would need to be scrupulously honest with yourself though. And you have to have a set protocol that will eliminate all variables other than your power.
Here is an example:
Never toss a coin at any time other than when you do a trial.
(This eliminates situations where you toss a coin but then decide you weren't ready)
Always toss the coin in the same environment with no distractions.
Toss the coin T times on each occasion.
(Your limit seems to be 6, so make it 4 to be sure you won't tire)
For simplicity, always make the coin come up heads.
(The sequence of all heads will be remarkable all on it's own)
(It also avoids situations where you may have forgotten what you picked)
Close you eyes.
(For blinding purposes

)
Concentrate for S seconds.
(you seem to be succeeding with S = 30 to 60 seconds)
Simultaneously juggle the coin a few times.
(Not sure if this is essential - you could always feel which side is heads)
Without opening your eyes, toss the coin C centimeters vertically into the air.
(To be a fair toss, I think C would need to be greater than 30 centimeters)
(If you accidentally throw it less, still count the trial)
Allow the coin to drop unimpeded onto a flat surface.
(A tight-knit carpeted surface is good to prevent the coin rolling away)
When the coin stops, open your eyes and record the result.
(Do not open your eyes untill the coin comes to a complete rest)
Always record the result of every coin toss.