In general, the simplest way to accomplish this is to use a sulfonic acid base cation-exchange material with a non-complexing eluent to elute monovalent species and then utilize a complexing eluent to elute copper.  The reference cited above from the Dionex website provides a general overview of methods optimized for transition metal chromatography but if you are simply after copper using a column such as the IonPac CS3 column with 100 mM methanesulfonic acid to elute monovalent cations followed by a suitable concentration of oxalic acid will allow for elution of copper without any monovalent cations present.  This assumes, of course, that you are using a post-column derivatization system with a UV-visible detector or an elemental spectroscopic detector since indirect conductivity detection generally won't work for copper at realistic copper concentrations.

You can see to this link: http://www.dionex.com/en-us/webdocs/4691-TN10_LPN032229-03.pdf

We are using IC only for determination basic inorganic cations. I think that you can changed composition of mobile phase in isocratic or gradient mode.

Main problem may be ammonium presence. Tray to switch to a chelating resin which will be selective towards copper even when complexed in solution, see e.g.

R.Caprioli, Journal of Chromatography A

Volume 640, Issues 1–2, 25 June 1993, Pages 365–369

In general, the simplest way to accomplish this is to use a sulfonic acid base cation-exchange material with a non-complexing eluent to elute monovalent species and then utilize a complexing eluent to elute copper.  The reference cited above from the Dionex website provides a general overview of methods optimized for transition metal chromatography but if you are simply after copper using a column such as the IonPac CS3 column with 100 mM methanesulfonic acid to elute monovalent cations followed by a suitable concentration of oxalic acid will allow for elution of copper without any monovalent cations present.  This assumes, of course, that you are using a post-column derivatization system with a UV-visible detector or an elemental spectroscopic detector since indirect conductivity detection generally won't work for copper at realistic copper concentrations.

Have you considered use a Cupric ion selective electrode?  The ability to measure Cu2+ concentrations will depend on the limits of detection, selectivity, sensitivity, etc, but it is something to consider if you haven't already looked into it.  I have use Ca2+ ISEs and they are very simple to use.

http://www.thermoscientific.com/en/product/orion-cupric-electrodes.html

Adsorption - desorption process can be applied to remove the copper ions. The cation-exchange medium has to be selectively  carried out. Again the level of the concentrations of the adsorbate has to be determined. This requires adsorption calculations. Reference can be made to relevant to  literature

Monovalent cations are easily removable using crown ethers. So you can do prior adsorption onto a crown ether and then later do analysis on IC. Alternatively, you can selectively adsorb Cu on a sulphur-containing adsorbent and later strip it for analysis. Another option would be to precipitate Cu e.g. using NaOH (more Na!), filtering this and redissolving the residue with acid to dissolve the precipitated Cu.

Thanks to all for worthy suggestions and comments. 

Infact im using IonPac SCS-1 column for the detection of Copper with 2mM MSA/0.5mM oxalic acid solution as eluent. As the copper concentation is very low (10 ppb to 1 ppm) so i use a pre-concentrator column Ionpac® TCC-2 to conc the solution that eventually increase the conc of Na and K also (which are already 20 and 10 ppm respectively, much higher than that of Cu conc.  so cant get a very good peak for Cu and also sometime its even difficult to get a good baseline.. 

i havnt tried Cupric ion selective electrode yet, but i will definitely look for it if i couldnt resolve issues with ion chromatography. 

Alternatively you can try to use chelation ion chromatographic methods. Iminodiacetic acid-based stationary phases (IMAC column stripped of metal) have strong affinity towards divalent and transition metal cations, while alkali metal cations elute unretained. DOI: 10.1016/j.chroma.2012.06.026 

A suggestion is to consider Dionex "OnGuard II Cartridges" for removing selected ions before IC.  There are several available for anions and cations and one or a combination may fit your needs.