Hi, a chara,
I don't know how much about Ogham or Irish you know, so here I'll take it that you don't know much, just in case
Firstly, the Ogham script was used to write Primitive Irish (c. 4th century until 7th century) rather than Modern Irish (compare Prim. VELITAS, Mod. FILE) which means that despite what you might find online or on souvenirs, it isn't suited for the current Roman spelling used today. The script doesn't indicate lenition (bh,ch,dh etc.) which are vital to modern Irish spelling, for example.
Now, if you want an Ogham tattoo you need to decide whether you want a Modern Irish word written in the script (which would be like transcribing Russian using Latin characters, for example) or a Primitive Irish word written in the script (even though the word may have to be reconstructed since it isn't attested).
Also, you might want to think more about what meaning in particular you mean with "family" as it can cover many meanings in English where Irish used different words altogether.
MOD. IRISH WORD:
Clann (< Old Irish
cland) means one's children, or the family that one produces so to say, i.e. progeny. It comes from Latin
planta (through Old Welsh
plant), like English "plant", implying offspring as an offshoot

(p is originally a foreign letter in Irish, btw).
The word can also mean "clan/tribe" (clan obviously comes from
clann) seeing as the Gaelic clans were typically united by a common ancestor, perceiving themselves as his descendants (which English "family" can encompass).
Many speakers and learners use this term for the modern concept of "the nuclear family", but this is historically inaccurate and, in my opinion, inadequate as a term. That's just my say in it though - "clann" would be perfectly understood as "family" amongst Irish speakers.
Teaghlach means "household", from Old Irish
teghlach <
techlach <
tech (modern
teach, meaning "house"). It is also used for "family", but really means something along the lines of "the people living under one roof". I'd probably use this for "nuclear family" in speech.
Muintir comes from Old Irish
muinter <
muntar/montar. It's etymology is disputed, possibly from Latin
monasterium "monastery", or from
*manu-tera "that which is under the hand, ie. the authority" or from native Celtic
*moni (Irish has
muin "protection"). This term can mean "family/household" (mo mhuintir = my family), or it can be used in a broader sense meaning people (muintir na háite = the locals, lit. people of the place) or followers united in some way or another.
Fine is another possibility, meaning "family group". It comes from Celtic
*weniyā ("family") from Proto-Indo-European (PIE)
*wenh₁- (“love, desire”), which gave Old English
wine (“friend”). That
wine is the second element of Lord of the Ring's
Éowyn (lit. horse-friend), btw

This word is also in the name of an Irish political party, Fine Gael (family of the Gaels). This word is a little outdated in my opinion - like you'd never hear someone say "m'fhine" meaning "my family (at home)" at all - but it's nice and broad for covering "family" as a tattoo.
Right, so there's a bit there to think about.
Here are pronunciation guides (more accurate IPA transcriptions, and rough English approximations) of the three main dialectal pronunciations of those four words:
Gaoth Dobhair (Gweedore, co. Donegal in northwest of Ireland - Ulster Dialect)
/kl̻ˠan̻ˠ/ "KLUHN"; /'tʲeː.l̻ˠah/ "TCHEY-lah"; /'mˠi.tʲiɾʲ/ "MWIH-tchir"; /'fʲi.nʲə/ "FIH-n(y)uh"
Conamara (Connemara, co. Galway in west of Ireland - Connacht Dialect)
/kl̻ˠaːn̻ˠ/ "KLAWN"; /'tʲa.l̻ˠəx/ "TCHA-luhkh"; /'mˠiːn̻ʲ.tʲəɾʲ/ "MWEEN-t(ch)ir"; /'fʲi.nʲə/ "FIH-n(y)uh"
Corca Dhuibhne (Dingle Peninsula, co. Kerry in southwest of Ireland - Munster Dialect)
/klˠaunˠ/ "CLOWN"; /'tʲai.lˠəx/ "TY-luhkh"; /'mˠiːn̻ʲ.tʲəɾʲ/ "MWEEN-tir"; /'fʲi.nʲə/ "FIH-nuh"
These words transcribed without change (letter for letter, though inaccurate) to Ogham are as follows:
clann > CLANN =
᚛ᚉᚂᚐᚅᚅ᚜teaghlach > TEAGHLACH =
᚛ᚈᚕᚌᚆᚂᚐᚉᚆ᚜muintir > MUINTIR =
᚛ᚋᚗᚅᚈᚔᚏ᚜fine > FINE =
᚛ᚃᚔᚅᚓ᚜With lenition and glide vowels removed:
clann > CLANN =
᚛ᚉᚂᚐᚅᚅ᚜ or with old irish CLAND =
᚛ᚉᚂᚐᚅᚇ᚜teaghlach > TEGLAC =
᚛ᚈᚓᚌᚂᚐᚉ᚜muintir > MUNTIR =
᚛ᚋᚒᚅᚈᚔᚏ᚜ fine > FINE =
᚛ᚃᚔᚅᚓ᚜PRIMITIVE IRISH WORD:
Now, if you'd prefer a word suited for Ogham script, I'd say using a primitive Irish word would be better. This stage in the development of Irish is very poorly documented, since it was only ever written down on Ogham standing stones (except when later found in academic scribal notes after it had progressed to Old Irish), and even then, most of the inscriptions are names.
This unfortunately means that for the tattoo, a word would need to be reconstructed. As a stand-alone word, "family" would need to be in the Nominative case, and the vast majority of Ogham is found in the Genitive case (indicating possession, like "John" in "Marcus son of John").
Right, now the problem is that none of these words bar
fine appear to predate Old Irish. So the most realistic reconstructed form would be:
fine < *weniyā; therefore maybe *VINIA =
᚛ᚃᚔᚅᚘ᚜ or earlier *VENIA =
᚛ᚃᚓᚅᚘ᚜; or without combined IA (ᚘ) symbol, *VINIA =
᚛ᚃᚔᚅᚔᚐ᚜ and *VENIA =
᚛ᚃᚓᚅᚔᚐ᚜For the others, I'll give possible transcribtions:
clann < cland > *CLAND =
᚛ᚉᚂᚐᚅᚇ᚜; or *QLAND =
᚛ᚊᚂᚐᚅᚇ᚜muintir < muinter > *MUNTER =
᚛ᚋᚒᚅᚈᚓᚏ᚜; or *MONTAR =
᚛ᚋᚑᚅᚈᚐᚏ᚜; or like QRIMITIR, *MUNTIR =
᚛ᚋᚒᚅᚈᚔᚏ᚜teaghlach < teglach < techlach > *TEGOLACO =
᚛ᚈᚓᚌᚑᚂᚐᚉᚑ᚜; or maybe *TEGOLACC =
᚛ᚈᚓᚌᚑᚂᚐᚉᚉ᚜Hope there's enough here for some more though on the tattoo!
