Many years ago, I bought a cheap set of dumbbells at one of those used
sporting goods stores. The finish is now starting to crack and peel in
some places. I'm wondering if there is some type of vinyl or similar
coating I can put on them to stop the deterioration.

My set goes from 2 lbs to 80 lbs. The ones from 30 lbs on up are hex
weights similar to this:

http://tinyurl.com/4o4n2t6

They appear to be solid metal. There is no deterioration with them.

The smaller ones are round and appear to have some sort of metallic
paint over a dark brown metal (iron?). There is minor chipping and
flaking in various places. One of the 15 lb weights actually has a bit
of a hole in the handle. The first picture below is low res, the
second is higher.

http://tinypic.com/r/14nohw6/7

http://tinypic.com/r/212bng2/7

Is there anything I can get that will stick to these and stand up to
some banging about?

What about Plasti-Dip, the stuff used to put a rubberized coat on tool
handles?

Will I need to first remove or at least roughen up the existing paint?

Or should I just used this as an excuse to convince the boss that I
need a set of those adjustable dumbbells?