In the list of names at Amboina in 1846 I only find the name H. Haijer (twice though) (link). Not more than a suggestion of a first initial.
They're there from 1842 onwards, Before then only a C. Haijer (already there in 1838), presumably Cornelis Haijer who died on Amboina in 1842.

I gather from other discussions here that a very important resource is the book mentioned here on Ambon, based on baptism records at Ambon. Whether that is relevant to your query I would not know though. [I just noticed a gap 1841-1883].

No, Cornelis Haijer died on 8.2.1842 and cannot have been the father but he may have been the grandfather.
The other births at Amboina with this surname are

Katharina Haijer b.6.5.1841
Hendrik Frederik Haijer b.1.8.1844 (probably died 20.12.1844)
Willem Laukens Haijer b.9.5.1845
Willem Gerrit Haijer b.2.2.1846 who married there in 1870
Diederik Haijer (child) died 17.6.1846

Have you found any further information on any of these besides Willem Gerrit?
Edit: A relevant marriage is not found there, whereas the marriage records can be searched from 1834 onwards. So it appears to me the parents got there from elsewhere in about 1840.
_{[Separate note - there are army records of 2 of the children of Willem Gerrit here (scroll down) just in case you did not have those.]}

Haijer named persons coming to Ned Indie before 1800: see

 https://www.nationaalarchief.nl/onderzoeken/index/nt00444?searchTerm=Haijer

In the index of the book Peter mentioned I found the following Haijer people: 

Haijer

Elizabeth Charlotta, AFY-I.

Jacoba Hermina, AFZ-I, BDW-.

Wilhelmina Cornelia, AGA-I.

Willem Gerrit, AGB-I, BWX-.

Unfortunally, I have not that book.

Given the birth in 1845 at Amboina of one Willem Laukens Haijer, possibly a brother of Willem Gerrit, and the birth in 1871 of a Loukens Hendrik Jacob Haijer, possibly a son of Willem Gerrit, I find suspicious the death on 20.7.1874 at Amboina of a Loukens Haijer, a military. Surely he must be related. But where is his army record? I have checked the Oost-Indisch boek online index and gone through the indexes of the suppletiefolio's. Can't find it. Where is it?

Wie weet te vinden de stamboekinschrijving van de militair Loukens Haijer die overleed op Amboina in 1874? Hij zal toch wel familie zijn, maar ik vind zijn stamboekinschrijving niet.

@ Peter,

IK heb ook gezocht en gezocht maar niets kunnen vinden via de stamboeken. Zal morgen nog eens een andere bron doorlopen.

mvg-Ben

Janssen's Indisch Repertorium geeft de volgende verwijzingen voor de naam Haijer:

Haijer : BRP/1 [32, 111, 124, 127, 159, 164];   GN/1956 [65];   INN/11 [190];   INN/26 [164];   INN/27 [239];

BRP/1 = Bronnenpublikaties van de Indische Genealogische Vereniging, dl. 1 : Genealogische bronnen betreffende Europeanen te Ambon, door P.A. Christiaans, 's-Gravenhage 1991.

GN/1956 = Gens Nostra jaargang 1956

INN/x = Indische Navorser nieuwe reeks, jaargang x

Er is op openarch ook een vermelding van M. Haijer ambtenaar in Ned Indie. Link

Aan het folionummer te zien komt hij vrij vroeg voor in het stamboek 1836-1940 en zou dus ook wel eens in de juiste periode in Ned. Indie geweest kunnen zijn.

Via de online index gevonden. Inderdaad de zoon van Willem Gerrit en Cornelia Lewerisa

Hij is in 1894 gesneuveld, maar er lijkt in de laatste kolom 1874 te staan. Misschien is dat de verwarring.

@Hans

The studbook that mentions M Haijer, registers civil servants. Unfortunately this studbook is not digitaly available, so no more details are available on line.

It can only be seen at the National Archive in the Hague or one can order scans. But making those scans wil carry some costs, and it is yet uncertain what information will be in it. (this is the link to the studbook that contains information about M. Haijer: link )

What you could do is to ask if somebody who lives in the Hague or is going to the National Archives shortly, wants to take a picture of the relevant pages of this stubook.

@Hans:

Are you familiar with this studbook registration of Pieter Jan Haijer, son of Elisabeth Charlotta Haijer?

Link to studbook entry Pieter Jan Haijer

According to the "Almanak en naamregister van Nederlandsch-Indie , 1840", the only person named Haijer that was living on Amboina (which was a VOC traing post by the way) was C. Haijer. Link

According to the "Almanak en naamregister van Nederlandsch-Indie , 1842" there were 2 persons called H. Haijer living on Amboina, link

Accoring to the "Almanak en naamregister van Nederlandsch-Indië , 1846", there were still 2 persons called H. Haijer living on Amboina, link
So one of them must be the father of Willem Gerrit.

I'll continue the search

I suspect there were indeed 2 persons "H Haijer" like for example a "Hans Haijer" and a "Hendrik Haijer"