Is there any tax due on the capital gains of selling a collectible coin on behalf of a relative, who is not a US citizen, and has never been to the US?

Assuming that   (a) you are  only acting as an agent  i.e. you facilitate the  exchange of  money for the  items and have no personal interest or gain from the transaction(s); (b) the  exchange/ transaction will occur in the USA; (c)  you are doing this as a hobby ; (d) the  articles have been brought into the country legally -----> generally IRS will view this as  US sourced income acquired by  a Non-Resident Alien. Thus  the  owner will have to file a form 1040-NR ( not supported by  TurboTax ).  It may be simpler for the person to give these to you as gift ( along with the  basis of the donor -- if it is worth more  $100,000 , you may have to file form 3520 - declaration of  gift from a foreign person ) , and then you sell the  items , report the capital gains on form 1040 ( supported by TurboTax),  the  foreign person then compensates you for the  taxes you paid.  Note that in the first  scenario -- your acting only as a go-in-between,  there is a flat 30% tax on net income whereas in the second scenario ( gift to you for subsequent disposition ) the gain is  treated as capital gain at your rate.  There are quite a few complications when you act as an agent  for a foreign person --- you need to withhold the taxes and also file  form 1042 .  Suggest you see a professional before take this step.