Line the holes with felt? Or do you mean line the side(s) of a
cylinder? Or put felt only at the bottom of the hole? A spray
adhesive, with a straw-tube (like the tube WD-40 has) might work.

How thick of felt? Felt on a pool table is as thin as upholstery
fabric, but felt for upper padding of coil springs (upholstered chair
seats, etc.) is 1/4" thick. How thick of felt are you wanting to
apply? I assume the felt is thin, like pool table felt. I know of
spray adhesive for upholstery applications. Maybe a local pool table
shop (repair shop) might have some good ideas for thin felt.

For the bottom of the hole, maybe the felt pads for furniture leg/
feet, with the peel and stick adhesive, will help. Wal-Mart or any
similar outlet has these peel and stick felt pads.

For inserting felt into a glue lined hole, wrap the felt around an
appropriate sized dowel rod and jam it in.

If you are wanting to line a hole for tool rests or some similar
object that needs to rest in a cushioned/lined hole, maybe your best
bet is to cut through the holes/cylinders, ie., 2 halves, line the
halves with felt, then re-attach the halves to make the whole
"holding unit".

Sonny