Some French sites have retained the phrase "pin press," so you could do that as well. I found a French site that translated pin press as "presse de broche." I have my concerns about that term because it seems to me that it would work better in the printing industry.

I found a Rumanian site that translates pin press as "presse pour pivots de fusée." Hopefully, this site is correct. And I did go on to find variation of the term used in other sites.

So, here are two translations for pin press. But I just don't know if they are the right ones for you :-)

References:
Automotive Seatbelt Retractor Pin Press Station [see picture]
The Pin Press Station automatically fastens spring and sensor covers to retractor assemblies. Only one operator is required to load and unload the retractor assembly.
http://www.metroautomation.com/Pages/cs-pinpress.html

Features: Pivot pin press station with press force monitoring, retaining clip press with clip orientation detection, rooster comb auto grease application and ergonomic workstation.
http://www.rdmachineandtool.com/Picture Gallery.htm

Position 2: Loads first machine pin press station
http://www.drsystemsinc.net/pdf_2/22-1 Pick and Place Fixed ...

Spring-loaded and locking pin press
http://fr.patentsdb.org/brevet/spring_loaded_and_locking_pin...

SUNNEN PIN PRESS. GREAT CONDITION
PRESSE DE BROCHE DE SUNNEN BP10 (UTILISÉ) TIGE
http://www.allstates.com/FrenchEngine.html

HYDRAULIC KING PIN PRESS
PRESSE POUR PIVOTS DE FUSEE
http://trucktool.ru/ftpgetfile.php?id=15

Presse à pivot
Presse de pivot de fusée FK 60 T
http://www.finkbeiner-france.fr/category/23254/33615

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Note added at 31 days (2009-03-06 03:26:47 GMT) Post-grading
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You're welcome, Spanenglish, and thank you :-)