Okay, there are a couple things you can do. One, you can run it inline with 1/8" OD tubing (what we generally use is twice that size, or 1/4"), and you'd need 1/16" inserts. SS-205-1 is the Swagelok product number for tubing insert for 1/8" OD and 1/16" ID. You'd also need 1/16" to 1/18" barb (or compression fitting - much more expensive) adapters.
The other thing you can do is use two 1/8" tube adapters. You'll need the SS adapters, as the airtight connection depends on the opposing metals being similar. SS-2-TA-1-2 is the Swagelok model number for a 1/8" tube to 1/8" male NPT adapter. On the intake end, you'll probably want that exact type, or the female type (substitute "7" for the "1"). On the output, you can go with male or female 1/8" NPT, or a 1/4" compression fitting (with 1/4 OD, 1/8 ID insert).
Check swagelok.com for more info, and do a google search for "tylok cross reference", which will give you a spreadsheet link with compatible model numbers of some of the competing brands (though it's missing several, at least). Swagelok sells direct, with a minimum shipping charge of $13 or so, but Evilbay is your best friend if you're willing to type in a bunch of different model numbers.