Use just normal Wire the coil is just there to stop oscillation and I never seen 2 of Simon coil that are the same they seem to get longer and whit more turns as time got by
Not criticising that is the way it is and if it works it works and I am sure Simon Know when it does and by the way yes I must confess and came out of the closet I had a look a lot of them that is just HiFi porn

but if you insist gogle up Advent materials the got it all. (well almost all one can imaging apart from copper plated silver but if one ask for it... I have used the insulated silver wire to make interconnects in the past There is no much current going trough that coil and the resistance is negligible the only thing is thick wire keep it's shape