Question

At the time when the Bill of Rights was written and used the phrase "an establishment of religion," what would the word "establishment" have meant?

Answer 1

It means the same thing as at anytime, so I would be very careful to answer this question with the political leanings of the inquisitor in mind: but the government cannot designate one religious sect as the state religion.

Answer 2

Actually, the word "establishment" as now commonly used would mean a building or an organization, such as a specific church. In 1789, "establishment" would have referred to the process of setting one specific church as the beneficiary of state approval.

Answer 3

establishment would also have been used to refer to a building or organization in the 1700's: http://www.etymonline.com/index.php?search=establishment&searchmode=none

Or other common meanings via Oxford English Dictionary...who knew establishment could be so flexible:

Established or stable condition; settlement, permanence; also, settled condition of mind, calmness, confidence. Obs.
1561 T. Norton tr. J. Calvin Inst. Christian Relig. i. 15 For it is merueilous, how great establishment groweth hereof.
1641 J. Jackson True Evang. Temper iii. 228 A succession of three good Princes together doth notably contribute to establishment, and felicity of a Kingdome.
1674 J. Owen Disc. Holy Spirit (1693) 69 Our Permanency and Establishment in the Truth.
1704 Clarendon's Hist. Rebellion III. xvi. 603 If God shall be pleased to add Establishment and Perpetuity to the Blessings he then Restored.
1782 J. Priestley Disquis. Matter & Spirit (ed. 2) I. Introd. p. vi, Truth will‥gain a firm establishment in the minds of all men.

Settled income, provision for a livelihood.
1726 Swift Gulliver I. i. vii. 126 His Excellency, who had the sole disposal of the Emperor's Revenue, might easily provide‥by gradually lessening your Establishment.
1776 Gibbon Decline & Fall I. xviii. 484 For each of these princes a suitable establishment was provided.
1776 W. Cowper Wks. (1837) XV. 34 It will afford me some sort of an establishment, at least for a time.
1832 H. Martineau Life in Wilds vii. 94 Providing a permanent establishment for the captain as their chief magistrate.