I'm wanting to customize a recurve bow for my daughter. She is wanting the limbs and stabilizer to be purple. I thought that I could either use shrink wrap or electrical tape for the stabilizer but not sure for the limbs.
There are a lot of companies which supply (and fit) custom vinyl wraps for virtually anything (mostly cars). I don't see why they couldn't do a set of limbs - should be able to wrap the limbs, stabs and riser as a colour matched set.
Look at the 3M UK site for details of vehicle vinyl wraps and they have a free search function for local wrappers - one of these may be able to do the bow with off cuts.
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Added bonus is wraps can be removed if/when your daughter decides to sell on her existing kit as she improves & upgrades.
Look up MDP supplies Ltd. That's where I get my vinyl from for arrow wraps. Comes off a big roll or sheets - just order what you want.
Personally, if you want it to look really nice go for hydrodipping.