From Robert C. Gouyet:

This coin can be from Henry I of Cyprus (1218-1253).  The legends are similar to some of his coins

THE ALISTAIR LILBURN COLLECTION OF COINS OF THE CRUSADES

Cyprus

Henry I (1218-1253), Electrum Bezant, type 3A, dies D/d, IC-XC, Christ seated facing on high-backed throne, rev hENRICI: REX CYPRI, king standing facing, 3.79g (CLC 7:4 [this coin]). Minor weakness, very fine, rare.

ex SCMB February 1981, P14

Origine : Baldwin, auction n°49, 09/2006, lot #1834

ROYAUME DE CHYPRE, Henri Ier (1218-1253), billon denier, Imitation au type de Gênes. Droit : + HENRICVS Castel génois. Revers : + REX CYPRI Croix pattée cantonnée de deux croissants et deux points. Ref.: Metcalf, 638; C.L.C. , 23, 5. 0,72g.

Origine : Elsen, vente publique n°76, 09/2003, lot #1165

You can find a similar crowned head on a coin of Henry VI and Frederick II of Sicily (1196-97)

 ITALIE, SICILE, Henri VI (1194-1197), billon denier, 1196-1197, Palerme ou Messine. Au nom d'Henri VI et de Frédéric II. Droit : + [..]· INP[..]RATOR Aigle éployée de face, tête à gauche. Revers : + FREDERIC' REX B. diad. de Frédéric de face. Ref.: Spahr, 32; M.E.C. XIV, 488. 0,50g.

 Origine : Elsen, vente sur liste n°228, juin 2004, lot #790.

From Erich Waeckerlin:

Regarding the first coin (aq229) presented under the heading "coins under discussion / Armenians of Cilicia" you may perhaps find the following remarks useful:

In spite of the similarity of the design with the denar of Levon I (Bedoukian #10), the coin is not of Armenian origin. It has been issued in the island of Cyprus by King Henry of Lusignan (probably Henry I, 1218-1253).

Av.: +HENRICVS:            [Henry]                        King's head

Rv.: +REX CYPRI             [King of Cyprus]         plain cross

References:

Schlumberger, Numismatique de l'Orient latin: pl. VI, 9 (and page 187)
Metcalf, Coinage of the Crusades: pl. 26, 656var (and pages 196-197)
Metcalf: Corpus of Lusignan Cpoinage I: pl. 30, 7 (and pages 113-116; attributed to Henry II)
Malloy/Preston/Seltman: CCS 27a (page 275)

Bibliography:

Gustave Schlumberger: Numismatique de l'Orient latin.
Paris: E. Leroux, 1878.
Reprint Graz: Akademische Druck- und Verlagsanstalt, 1954.

D.M. Metcalf: Coinage of the Crusades and the Latin East in the Ashmolean Museum Oxford.
2nd edition, London: Royal Numismatic Society, 1995.

D.M. Metcalf: The White Bezants and Deniers of Cyprus 1192 - 1285.
Nicosia: Cyprus Research Centre, 1998.
Corpus of Lusignan Coinage, Vol. I

Alex G. Malloy, Irene Fraley Preston, A.J. Seltman: Coins of the Crusader States 1098 - 1291.
Second edition, Fairfield CT: Berman Publications, 2004.