Nylon fibers are mainly dyed with acid dye. But due to the less number of amino (-NH2) group than wool (approximately 6 times lower) deep shade cannot produce by acid dye due to lower exhaustion.
One of the ways this has been acheived industrially has been to use hydrophobic acid dyes. A variety of which have been manufactured on an industrial scale. If you are just trying things out, look for monosulfonated acid dyes, or acid dyes with long alkyl substituents. Alternatively, the topic is discussed in a recent book published by Wiley, Coloration of wool and other keratin fibres, eds Lewis + Rippon.
Thanks Richard W Horobin for your answer. Instead of monosulfonated acid dyes is there any way to increase the amino group of nylon fiber by modification?
Do you mean how could you take a routine nylon sample and increase its content of amino groups? Well, I am not a textile chemist [my expertise is rather in the interaction of dyes with biological material ... close, when considering wool or cotton, but ...] so you probably need to attract the attention of someone else.
BUT just eyeballing the classical nylon structure, it has a terminal amino and a terminal carboxyl. So maybe you converted the terminal NH2 into, say, N[CH3]3+ by treatment with some methylating agent such as methyl iodide, then the polymer would perhaps be likely to take up anionic dyes even under neutral conditions.