I would make a post about it and state the facts about the cost of running the site.
Stress that the forum will remain to be free for all to use and enjoy.
Then something like:
Anyone who enjoys the site and would like to contribute to the operation of the site - your help would be appreciated. Any donation helps reduce the out of pocket costs.
Anyone who contributes ANY amount will get a "Sponsor" title or whatever.
When you leave it up for them to decide what the site is worth to them... you just might be surprised. On a support site I take care of, we did something similar. Yes, we got $5 and $10 contributions which are great. But we also got surprises of an occational $100 or even $500 donation. Sometimes you might be surprised what your site and your community is worth to some people.
But pointing it out is the way that
a) people know they can donate and help
b) you can counteract the "what's this site coming to" by stating the reasons and that your intent is that it will alway be free, contribution is voluntary.
c) You can tell them what supporters get.
On the one site I took care of - we had "SOS Sponsors". SOS stood for Save our Site. You'd be surprised how many people
want the SOS Sponsor title once they start seeing others with them.
And again - it doesn't matter if they give $5 or $500 - nobody but you knows.
Above that - some sites do a bronze/silver/gold type of thing, with different donation levels.
One more tip - if you're creating buttons in paypal - you can create a freeform donation button. But don't sell yourself short. Create a $5, $10, $15 whatever RECURRING button. As in $5 per month. People will do it once and forget until you remind them, but I found many people want to
regularly contribute a small amount. And the paypal recurring payments/subscriptions is a great way to do it.