I have run many miles with a SCCY 9mm in a belly band. I find that having the gun at exactly 3 O'Clock and secured under the waistband of my running shorts minimizes bouncing and wiggling.
What I have done is to secure a cheap plastic IWB holster into the elastic pocket on the belly band. I replaced the clip with a loop of nylon webbing that wraps around the "pocket" in the belly band material. The pistol clicks into place in the plastic holster and is secure.
With anything much heavier than the SCCY (15 ounces empty) the gun just bounces too much for me. Something lighter such as a pocket 380 would likely carry much easier.
You'll also need to consider the impact of moisture, sweat and dirt on the gun. I would imagine that a stainless or corrosion resistant gun would be an absolute necessity.
I have carried a heavier gun in a runner's fanny pack in both front and back. The strap needs to be crazy tight to keep that pack from bouncing around. Tighten it until until you are sure that it is too tight - and then tighten it some more.
YMMV.