Tetrabutylammonium peroxydisulfate (made from tetrabutylammonium hydrogen sulfate and sodium peroxydisulfate) and iodine are used to iodinate phenol exclusively in the
para- position in 92% yield. 1,4-Dimethoxybenzene is also monoiodinated in 92% yield.
The experimental from the following articles was posted some time ago by foxy2 in
Post 199741 (missing)
(foxy2: "Para-Selective Iodination of Methoxybenzenes", Chemistry Discourse), but the full articles fit nicely into this thread. The second article deals with the preparation of the oxidising agent:
A Practical Iodination of Aromatic Compounds Using Tetrabutylammonium Peroxydisulfate and IodineSeung Gak Yang and Yong Hae Kim*
Tetrahedron Letters,
40 (1999), 6051-6054
AbstractA variety of aromatic compounds substituted with an electron donating group such as methoxy, hydroxy, or amino group, were regioselectively iodinated with iodine in the presence of tetrabutylammonium peroxydisulfate under mild conditions in excellent yields.

Novel Direct Tetrahydropyranylation of Alcohols with Tetrahydropyran and Tetra-n-butylammonium peroxydisulfateHyun Chul Choi, Kyu Il Cho, and Yong Hae Kim*
Synlett,
1995, 207-208

Another interesting method is the use of N-iodosaccharin for the iodination of arenes, and also - perhaps more interestingly - for the hypoiodination of alkenes to give iodohydrins in excellent yields:
N-Iodosaccharin - a New Reagent for Iodination of Alkenes and Activated AromaticsDarko Dolenc
Synlett,
2000, 544-546
AbstractA mild and efficient iodination reagent, N-iodosaccharin was prepared. Iodination of activated aromatics and alkenes with the reagent takes place fast and under very mild conditions, without the aid of strong acids or heavy metals. The reagent does not affect oxidizable groups, such as hydroxyl or aldehyde.
