That's pretty much what a Phillips pellet holder is...
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No longer available at most places but you can put one together from walmart arts and crafts/ sewing department stuff easy enough
 
As stated above foam. Ive bought foam off amazon and ebay with adhesive backing and then a pair of leather punch pliers from Harbor freight to pick whatever size hole you want and bam.
Make whatever size and shape of foam and punch out hole smaller than whatever pellet your wanting to carry.
Otherwise 3D print something, ive seen TPU rings that go on turrets and in that manner you could make a box that attaches somewhere or other clamp on devices that have a flat panel that you can attach the foam to! Limitless really.
Another non intrusive device is a neck pouch like we use in field target.
 
Maybe a little pouch on your belt a to dump a tin in and pinch out a pellet as needed?


 
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