In The Unicode Standard, Cypriot syllabary implementation is discussed in  Chapter 8 Europe-II: Ancient and Other Scripts.

The Cypriot syllabary was encoded in The Unicode Standard version 4.0. The script is encoded in one block. It also requires a second block for Aegean numbers which are used in several scripts:

Blocks Character Range Added in Unicode Version Unicode Chart
Cypriot Syllabary 10800..1083F 4.0  U10800.pdf
Aegean Numbers 10100..1013F 4.0  U10100.pdf

A number of proposals for its inclusion were submitted to the Unicode Technical Committee and WG2:

1997-05-22 Proposal to add Cypriot Syllabary to Unicode/ISO-IEC 10646 — John H. Jenkins ( L2/97-108)

1997-06-10 Overview of the Aegean scripts — John H. Jenkins ( WG2 N1575,  L2/97-105)

2000-02-15 Scripts from the Past in Future Versions of Unicode — Carl-Martin Bunz ( L2/00-128)

2000-04-26 Further comments on historic scripts — Carl-Martin Bunz ( L2/00-153)

2001-01-28 Status Report on Aegean Script Proposal (Linear B, Aegean Numbers and Cypriot Syllabary) — Deborah Anderson ( L2/01-084)

2001-04-03 Revised proposal to encode Aegean scripts in the UCS — Deborah Anderson, Michael Everson ( WG2 N2327,  L2/01-149)

2001-05-20 Status Report on Aegean Script Proposal (Linear B, Aegean Numbers and Cypriot Syllabary) — Deborah Anderson ( L2/01-217)

2001-10-03 Final proposal to encode Aegean scripts in the UCS — Deborah Anderson, Michael Everson ( WG2 N2378,  L2/01-370)

2002-04-27 Status Report on Aegean Script Proposal and the Submission by the Thesaurus Linguae Graecae (TLG) — Deborah Anderson ( L2/02-160)

2002-05-01 Aegean Script Proposal (notes) — Deborah Anderson ( L2/02-191)

2002-05-09 Request for changes in Aegean Scripts — Deborah Anderson, Rick McGowan ( WG2 N2455.doc,  L2/02-207)

2012-11-03 Sorting all RTL scripts together — Roozbeh Pournader ( L2/12-377)